text:
Mass relations in chemistry and stoichiometry

The Mole Concept
To begin with chemical relations to mass, perhaps the most important idea to understand is the mole concept. We begin by looking at an example from the periodic table:

The atomic mass is our primary concern here. By definition, a mole (symbolized as mol) is the quantitative amount of any given substance that contains as many atoms, molecules, or formula units as the number of atoms in exactly 12 g of carbon-12. This number is known as Avogadro's number (usually symbolized as NA), and has recently been given the value of 6.0221367 × 1023.

In this sense then, we might equate the term mole to dozen. With previous experience, we know that in a carton of a dozen eggs, you get twelve individual eggs. The same is said with the mole: for every 1 mole of a given substance, you have approximately 6.022 × 1023 atoms/formula units/molecules in the sample amount. As you will learn later, the mole is very important in many calculations involving concentrations of substances, osmotic pressure, chemical kinetics, and equilibrium.

The main idea that must be understood is that for 1 mole of any substance, we have Avogadro's number of molecules, atoms, or formula units. Consider the chemical formula for water, H2O. If we have one mole of H2O, then we have approximately 6.022 × 1023 different H2O molecules. To continue further, we notice that there are two hydrogen atoms for every one oxygen atom in one formula unit of water, therefore we can say that there are approximately 1 × 6.022 × 1023 oxygen atoms and 2 × 6.022 × 1023 (1.204 × 1024) hydrogen atoms present in one mole of water.

So how do we calculate the molar mass of H2O? Simple. This is where the atomic mass is most important. On the periodic table we retrieve the atomic masses of hydrogen and oxygen, which are 1.00794 amu and 15.9994 amu respectively. (Note that "amu" stands for atomic mass units and has the units of g/mol). The atomic mass for a given substance is equal to one mole, and therefore contains roughly Avogadro's number of atoms/molecules/formula units. With this in mind, we add the following:

2(Atomic Mass of Hydrogen) + Atomic Mass of Oxygen = Molecular Mass of H2O 2(1.00794) + 15.9994 = 18.0152 g/mol

If you understood that, congratulations - you've completed your first stoichiometric calculation.

Stoichiometry
Chemistry is a wonderful thing - and one of its least wonderful yet most important concepts is stoichiometry. Stoichiometry is the calculation of quantities of reactants and products involved in a chemical reaction. Too wordy? Let's make peanut butter and jelly sandwiches.

Think of how you make a PB&J sandwich - do you just slop the stuff together and hope it turns out right? Of course not! You take two pieces of bread, a tablespoon of peanut butter, and a table spoon of jelly, and there you have it. This is what stoichiometry is about: it's the recipe that counts, too.

So if we had an equation for a peanut butter and jelly sandwich, it might look like this: Pb + J + 2Bread → PbJBread2

However, let's look at a real balanced chemical equation:

2C3H8 + 10O2 → 6CO2 + 8H2O

What are those numbers in front of the compounds? In chemistry, we call these numbers coefficients which serve to balance out the amount of each individual type of atom on both sides (for example, there must be the same number of carbon atoms on the left side as there are on the right side of the equation).

So back to our equation:

2C3H8 + 10O2 → 6CO2 + 8H2O

The easiest way to read it would be: "When you have two propane molecules (C3H8) and ten molecules of diatomic oxygen (O2), you get six molecules of carbon dioxide (CO2) and eight water molecules (H2O)". Just like a recipe. Remember that in this scenario, molecules could possibly even be replaced with moles as well.

Now for an example. Let's take the same reaction with propane and oxygen: if you have 10 g of propane, how much carbon dioxide do you produce?

Believe it or not, this problem is very easy, and with some practice, you could become a professional at this. First, we look at the ratio of propane to carbon dioxide - which is 2 propanes for every 6 carbon dioxides, or in fraction: 2/6 (do not reduce).

Let's start the calculation:

Notice the ratio of moles of propane to moles of carbon dioxide. This is called the key step. One might consider this part of the calculation a sort of "stepping stone" from one compound to the next.

Let's see how much H2O we can get from 10 g of propane:

Now suppose we have 15 g of H2O - how many grams of oxygen are there? Even though H2O is a product, we can still work the problem the same way, but in reverse:

Note: you may have noticed that the molecular mass for O2 is 32.00 rather than 15.999. There's a reason for this: gaseous oxygen is diatomic, meaning that in it's gaseous state, each oxygen molecule is comprised of two oxygen atoms that have been covalently bonded together.

There are several different diatomic elements, and a simple way of memorizing them is through the acronym "Br I N C H O F" (pronounced "brink-hoff"), which represents the seven diatomic molecules.   Br2 - Bromine   I2 - Iodine   N2 - Nitrogen   Cl2 - Chlorine   H2 - Hydrogen   O2 - Oxygen   F2 - Fluorine

From here, stoichiometry only gets more complicated (but not necessarily more difficult). As said before - with practice, these calculations can become second nature.


text:
Electronic structure

Electrons were believed to be particles until Louis de Broglie in 1924 suggested they have wavelike properties as well. A few years later Schrödinger calculated the energy of an electron in a hydrogen atom by using an equation that treated the electron like a wave. He obtained a series of energy levels, instead of a single energy — which means we can't tell where exactly an electron is located. We can only know where the electron is likely to be.

Classical (Newtonian) Structure
The basic electronic structure of atoms is that of energy levels, also called shells. These levels are certain distances away from the nucleus of the atom; the higher the level, the higher the energy of the electrons. The first energy level can hold up to two electrons, the second can hold up to eight, the third can hold 18, the fourth can hold 32, and shell n can hold 2n2 electrons. For neutral atoms (those with no charge (not ions)), the number of electrons is equal to the atomic number of the atom.

The Bohr Model
Niels Bohr was a pretty smart guy. He came up with a theory that atoms were composed of even smaller particles, with negatively charged electrons orbiting a small but massive positively charged nucleus, much like the earth orbits the sun. While this makes sense, it turns out that the real case is more complicated than even Bohr could imagine.

Quantum numbers
There are a set of four dimensionless quantum numbers'' associated with each electron in an atom. The principle quantum number is n, as mentioned above, and it is limited to positive integer values. The azimuthal quantum number l has a value of at most n-1, and it must be a non-negative integer (0 is a possible value). The magnetic quantum number ml may range from -l to +l in value. The spin project quantum number ms is the only one of the four whose domain does not depend on n, and it may only have values of either +1/2 or -1/2.''

Subshell nomenclature
Where l=0, the electron subshell is an s orbital. Where l=1, the electron subshell consists of 3 p orbitals. Where l=2, the electron subshell consists of 5 d orbitals. Where l=3, the electron subshell consists of 7 f orbitals. In hypothetical atoms, where l=4, the electron subshell is 9 g orbitals. The number of orbitals of a kind in the subshell is the number of possible ml values that subshell has. The higher the value of l for a particular subshell kind, the higher the n value must be for that subshell to exist at that energy level. This is because l has a maximum value of n-1, and for a particular kind of orbital, n must be a minimum value so l can have the requisite value.

The Pauli Exclusion Principle states that no two electrons in the same atom may have the same set of quantum numbers. Therefore, only two electrons at most may occupy any single orbital, because each orbital has the same n, l, and ml values, leaving only ms to vary (which only has two possible values).

Each subshell is denoted by n[orbital]; hydrogen's electron, for example, lies in the 1s orbital. Because each orbital can hold two electrons, the maximum number of electrons in a particular subshell is the number of orbitals in that subshell times 2. For example, the 2p and 3p subshells may each hold 2 electrons/orbital*(3 p orbitals)=6 electrons.

The Aufbau Principle states that the lowest-level subshells are filled before higher-level subshells in the ground state of the atom. For example, helium has 2 electrons total, and they fit into the 1s level. If either were in the 2s subshell, this would not be the ground state because the 2s subshell is filled before the 1s subshell is completely filled.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Electronic structure


text:
Ionic bond

Ionic bonding occurs when an atom or molecule completely transfers electrons to another atom or molecule. This happens because the valence electron of what becomes the cation is attracted to what becomes the anion. This transfer of electrons causes electrostatic attraction; the receiving atom or molecule develops a negative charge to become an anion, and the transferring atom or molecule a positive charge to become a cation. The atoms and/or molecules, now having opposite charges, are attracted to each other, thus forming an ionic bond. Some examples of compounds with ionic bonds are NaCl (sodium chloride or table salt), and CaCO3 (calcium carbonate). Such compounds are called ionic compounds, as opposed to covalent or molecular compounds which have no ionic bonds at all.

The charge of a cation or anion is denoted as a superscript after the formula of the ion. A + sign denotes a positive charge resulting from loss of electrons. A - sign denotes a negative charge resulting from gain of electrons. The number of electrons missing or gained is written before the + or - sign to indicate the degree of charge; when a + or - sign is seen alone in the superscript, the charge 1+ or 1- respectively is implied. For example, the cation of NaCl is Na+, while the anion of CaCO3 is CO32-.

Typically, metals form the cation and nonmetals the anion, but there are exceptions. In ammonium chloride (NH4Cl), for example, the cation is NH4+, which is completely made of nonmentals.

Examples
When neutral single atoms of Na and Cl come together, the sodium atom may transfer a negatively-charged electron to the chlorine (see animation below). This leaves a positive charge on the sodium, and a negative on the chlorine, creating Na+ and Cl−. These charged atoms are called ions, and they will be attracted towards each other, forming an ion pair of sodium chloride. This attraction of oppositely-charged ions is called an ionic bond.

When a molecule picks up or loses one or more electrons, the result is a polyatomic ion. CO32- is a polyatomic ion consisting of a central carbon atom bonded to three oxygen atoms. Its overall charge is -2, having two more electrons than the total of what the carbon and oxygen atoms would normally have.

Two ionic compounds can switch their cations and anions in a double replacement or metathesis reaction. For example, solutions of barium nitrate and sodium sulfate can be mixed to precipitate solid barium sulfate: Ba(NO3)2+Na2SO4 → BaSO4+2NaNO3.

A free element can replace another element or polyatomic ion as the cation or anion of an ionic compound in a single replacement reaction: 2Fe2O3+2Al→Al2O3+2Fe 2NaBr+Cl2→2NaCl+Br2 In either case, ions that do not change in the formation of new ionic compounds are spectator ions; the Na+ ion in the latter example remains unchanged except being ionically bonded to a different anions.

Properties of ionic compounds
Because of the strong binding of the crystal lattice of most ionic compounds, and well-packing, they tend to have very high boiling and melting points. Ionic compounds do not conduct electricity while dry, but when the ions are separated in solution, they conduct electricity well. Ionic compounds tend to dissolve in substances with polar covalent bonds, such as water. Most do not dissolve in non-polar compounds like (CH4). For what is meant by "polar" or "non-polar", see covalent bond.

Differing between ionic and covalent bonds
Although ionic and covalent bonds are generally considered separately, there exists substantial grey zone between them. Beryllium chloride (BeCl2), which one might expect to be ionic, actually has significant covalent character.

In general, although metals tend to form ionic bonds with most nonmetals, the electronegativity differences between the bonding elements is what determines the degree of covalency of a bond. Electronegativity, for our purposes here, can be defined loosely as the affinity of the atom for the electron pair in a bond with another atom. Fluorine is the most electronegative element, assigned a dimensionless electronegativity value of 4.0. Caesium is the least electronegative non-radioactive element (francium may be less electronegative but is highly radioactive), with a value of .7. The smaller the electronegativity difference, the greater likelihood of a covalent bond.

Likewise, there is only a certain degree in which metals, especially transition metals, can completely lose electrons. For example, ruthenium tetroxide (RuO4) is highly covalent, even though oxygen is much more electronegative than ruthenium, because even oxygen cannot completely take all 8 of the electrons ruthenium uses to bond. Lacking the electronegativity for this, oxygen must settle for double covalent bonds. On the other hand, ruthenium dioxide (RuO2) is, for the most part, ionic, as only 4 electrons have to be contributed to bonding by ruthenium.

title: Ionic bond


text:
Covalent bonding

A covalent bond is a form of chemical bonding which is characterized by the sharing of electrons between atoms. Covalent bonds are mainly formed due to the tendency of the elements to attain a completely filled outer shell, that is, attain noble gas configuration and become stable.

Elements forming covalent compounds achieve noble gas configuration by sharing electrons within the atoms, unlike ionic compounds which achieve the noble gas configuration either by gaining or losing electrons from the outermost electron shell. In covalent bonds, when two atoms are in need of extra electrons to fill their outer valence electron shell, they will often share an electron. The most common example that most people are familiar with is water. The oxygen in water forms a covalent bond with the hydrogen, thus filling the hydrogen's outer shell with two electrons (this is because the outer shell of hydrogen has a maximum capacity of two electrons). While an oxygen atom, originally having six outer electrons, now has seven valence electrons, it requires another in order to fill the shell, and so it bonds with another hydrogen to form H2O. Oxygen, thus has attained the configuration of the noble gas neon and the hydrogen atoms have obtained the configuration of the noble gas helium.

Covalent bonding does not produce electrons, it simply pairs them so that each atom has access to at least one more valence electron than before the bond.

Covalent bonding occurs between atoms with similar electronegativity, and thus most often occurs between non-metals. However, as there are sometimes uneven distributions of electronegativity, either one of the elements in any given compound may attract the shared electrons closer to it than the other one. Therefore, it will have more of a negative charge than the other (while the other becomes more positive). Though this is not a charge to the extent of ions when they gain/lose electrons, due to the slight charge, covalent compounds can produce ionic properties.

A simple way to understand the concept of a covalent bond is, Co can be taken as "co-operation" or "jointly" and valence, so covalent means the co-operation or joining of valence electrons.

Types of Covalent Bonds
The bonds formed by sharing of an electron pair between two atoms can typically be single, double or triple; that is, in covalent bonds, atoms may be linked together by single, double or triple bonds.However there is also quadruple covalent bond. In simplest terms, "single", "double", and "triple" refer to the number of shared electron pairs in the bond. For example, in the dioxygen (O2) molecule, each oxygen must share two of its electrons in order to obtain the noble gas configuration of 8 valence electrons, resulting in a double bond of two shared electron pairs. The valency of an atom is the maximum number of bonds it can form, usually the number of electrons required to reach a stable noble gas configuration (there are exceptions to this rule, called the octet rule as all noble gases except helium have 8 valence electrons, discussed further down). Each double bond counts as 2 bonds for this purpose, and each triple bond counts as 3.

Whether a bond is single, double, or triple is its bond order.

Single Covalent Bond
In some molecules, a shared pair of electrons are contributed between the atoms, thus creating a "single bond". For example, in a hydrogen molecule, the two atoms of hydrogen are bonded together by a single bond.

How? The valency of hydrogen is 1, that is, the number of electrons present in the outermost shell is 1 and it needs 1 more electron to attain a noble gas configuration, that is a completely filled outer shell.

H has a valency of 1 and it needs 1 more electron to become stable. So, it forms a bond with another hydrogen atom and shares its electron with it and the second hydrogen atom shares its 1 electron with the first one,

( H x)               (x H )

(Here, x shows the number of electrons present in the outer shell of a hydrogen atom.) Now, the first atom shares its one electron with the second hydrogen atom and the second atom shares its one electron with the first one and thus we get one hydrogen atom.

( H (xx) H )

Thus, 2 atoms of hydrogen share their electron to form a molecule of hydrogen, H2. This allows each hydrogen atom to attain the electronic configuration of the noble gas helium. The shared pair of electrons is said to constitute a single bond within the two hydrogen atoms. It is a single bond because only one pair of electrons are shared within the hydrogen atoms. A single bond is denoted by a single line between the atoms. For example, the covalent bond in a hydrogen molecule is represented by:- H—H Such single covalent bond is also formed in chlorine molecule, Cl2.

Double covalent bonds
Sometimes, two atoms share two, not just one, electron pairs to attain a noble gas configuration, with each atom contributing two electrons for a total of four bonding electrons. The minimum valency of an atom that can participate in this kind of covalent bonding must have a minimum valence of 2. O has a valency of 2, with 6 electrons, needing 2 more to become stable (although oxygen has 6 electrons, it has a valency of 2 because it only needs 2 more for stability). It therefore can form a double bond with another oxygen atom, with each atom keeping 4 of its electrons uninvolved in bonding and sharing 2 with the other atom.

(xxxx O xx)               (xx O xxxx) thus becomes: (xxxx O (xxxx) O xxxx) 4 kept electrons plus 4 shared electrons then equals a stable 8-electron configuration. A double bond is denoted by a doubled line between the bonding atoms: O=O Such a double bond is also found in the carbon dioxide molecule CO2:

(xxxx O (xxxx) C (xxxx) O xxxx) Here, each oxygen atom double-bonds to the carbon atom. The carbon atom has 4 valence electrons, and since it needs 4 more, it has a valency of 4, allowing it to form 2 double bonds (or 4 total bonds): O=C=O

Triple covalent bonds
Likewise, when two atoms share three electron pairs, the bonding interaction is a triple bond. The minimum valency of an atom that can participate in this kind of bonding must be a minimum of 3.

N has a valency of 3, with 5 electrons, needing 3 more to become stable. It can form a triple bond with another nitrogen atom, with each atom sharing a total of 6 electrons with 2 unshared, making a full octet. (xx N xxx)                (xxx N xx) bonds to form: (xx N (xxxxxx) N xx) A triple bond is denoted by three lines connecting the bonding atoms:

Exceptions to the octet rule
Often one or more bonding atoms in a molecule do not satisfy the octet rule, even though the atom is stable with respect to its electron configuration.

For example, sulfur ( S ) has 6 valence electrons like oxygen. One might expect it to always share two to gain a noble gas configuration, but in sulfur hexafluoride (SF6), it shares all six of its valence electrons in single bonds with fluorine, thus exceeding the octet rule by 4 electrons: Likewise, sometimes an atom might have less than a full octet. Most elements that are not in the main groups (IA, IIA, IIIA-VIIA) don't follow the octet rule in this manner, and group IIIA elements also tend to have less than an octet.

Boron ( B ) has 3 valence electrons, needing either 5 more or 3 less to achieve a noble gas configuration. However, gaining 5 is not very easy (although it is possible, discussed later) while boron is too electronegative to fully lose all three.

Therefore, boron has a valency of 3 and shares all three valence electrons. However, other atoms can only share 3 total additional electrons with boron for a total of 6 - 2 short of the octet rule. Boron compounds of this kind are nevertheless stable. One example is boron trichloride (BCl3): The third and least-common violation of the octet rule occurs for molecules where the total valence electron count is an odd number. This makes complete electron pairing impossible and it is not possible to achieve a full octet For example, nitrogen monoxide (NO) has a total of 11 valence electrons. Nitrogen and oxygen easily share two electrons each, but nitrogen still needs a third electron. Oxygen and nitrogen can then be said to be sharing a third electron contributed from oxygen that is unpaired. However, this is not a replacement for a full electron pair and this is not a triple bond. It is more than a double bond, though, and can be called a "2 and a half" bond, where the dashed line represents the "half-bond" (this terminology is not exactly correct but sufficient for this example): As might be expected from the presence of an unpaired electron, odd-number-electron molecules tend to be reactive, as they are made more stable if their unpaired electron is paired.

Dative covalent bonds
The bonding pair of electrons need not come from both atoms. In some cases a single atom supplies both electrons shared in a bond. In carbon monoxide (CO), oxygen has 6 valence electrons and carbon 4 valence electrons. If each atom shares two electrons each, then oxygen satisfies the octet rule but carbon is still in need of two. (xx C xx) (xx O xxxx) (xx C (xxxx) O xxxx) Oxygen thus will share two more of its electrons with carbon, forming an additional bond with the pair of electrons entirely contributed from oxygen. This bond is a dative covalent bond. The electrons in question are highlighted in green. (xx C (xxxxxx) O xx) This additional bond adds on to the two bonds already made, so this is a triple bond, albeit an unusual one where the atoms don't make equal contributions to the bonding. It is represented like any other triple bond: Dative covalent bonds can also allow boron to achieve a complete octet. Boron trifluoride, with the same structure as boron trichloride (mentioned above), can react with ammonia (NH3), where nitrogen has 2 unshared electrons. The boron atom can link up to nitrogen in a dative covalent bond using those electrons:

title: Covalent bonding


text:
Gases and gas laws

Gases and their Properties
A gas is a state of matter with unique physical properties.

Gases assume the volume and the shape of their container and as such mix evenly and completely. In addition, a gas is the most compressible state of matter (having the lowest density).

The individual molecules which make up a gas can make collisions with the edges of their containers. As such, they exert a force on the container. We call this force the pressure of a gas.

Gasses are the only state of matter that are governed by universal laws. The universal gas constant, R, is unique in that it has relevance to all gasses.

Ideal Gases
A hypothetical "ideal" gas would satisfy the following requirements:

1. A gas molecule has neglible volume, and is separated from other molecules in a gas by distances far greater than its own size.

2. A gas molecule travels in random directions and frequently collide with other gas molecules. These collisions are perfectly elastic, which means that kinetic energy is conserved.

3. Gases exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of the molecules is proportional to the temperature of the gas.

However, gases do exert forces on one another: that is how they can condense into liquids. And a gas does have volume which is not negligible. This is deviation from ideal behavior (real gas behavior).

Gas Laws
The following gas laws assume ideal behavior:

Avogadro's Law: If temperature and pressure are constant, then the amount of moles of gas in a system is directly proportional to the volume of the system.
 * $$\qquad {n}$$ represents the number of moles in the system. $$\qquad {V}$$ represents the volume of the system.
 * $$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$.

Boyle's Law: If temperature and the number of moles of gas are constant, then the pressure of a system is inversely proportional to the volume of the system.
 * $$\qquad {P}$$ represents the pressure of the system. $$\qquad {V}$$ represents the volume of the system.
 * $$ \qquad P_1V_1 = P_2V_2$$

Charles's Law: If pressure and the number of moles are constant, then the volume of a system is directly proportional to the temperature of the system.
 * $$\qquad {T}$$ represents the temperature of the system. $$\qquad {V}$$ represents the volume of the system.
 * $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$.

Gay-Lussac's Law: If volume and the number of moles of gas are constant, then the pressure of a system is directly proportional to the tempreature of the system.
 * $$\qquad {T}$$ represents the temperature of the system. $$\qquad {P}$$ represents the pressure of the system.
 * $$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$

The Ideal Gas Law: When we combine together the above laws, we get the ideal gas equation, where P is pressure, V is volume, n is moles, T is temperature, and R is the gas constant, which has various values depending on the unit on pressure:

$$\qquad PV=nRT$$

However, if we take into account some real behavior, we can get an improved version of the Ideal Gas Law. The observed pressure is less than the ideal gas law predicts because the molecules do have interactions with each other, and when they do, it will reduce collisions with the container, and low pressure. The volume is bigger than it should be, because the molecules take up space, which must be accounted for. So, the corrected equation, known as the van der Waals equation, is

$$(P+a\frac{n^2}{V^2})(V-bn)=nRT$$

The value of a depends on how strong the interactions are between molecules. The value of b is related to the size of the molecule. The term bn approximates the excluded volume that is associated with the finite volume that the molecules would occupy.

Many other equations exist relating pressure, temperature and volume of gases. These equations of state are empirically derived and attempt to correct for the real behavior of gases. Some of these equations of state include: Redlich-Kwong, Soave-Redlich-Kwong, Peng-Robertson and the Virial equations of state among others.

Lab(s)

 * /Boyle's law lab/ that measure atmospheric pressure using a hospital syring with weights used to enhance pressure.

title: Gases and gas laws


text:
Chemical kinetics

Chemical kinetics is the study of the rate of a chemical reaction. For any given reaction: A + B → Products Kinetics can answer:
 * How quick is A consumed?
 * How quick are the Products produced?
 * What can we learn about the reaction mechanism?

Chemical Kinetics
When we say "chemical kinetics", we mean that we are studying the rates of reaction, and what affects the rates. Chemists have been able to establish a fairly accurate way of predicting how long it will actually take for a reaction to move to completion (meaning there is no reaction going in the direction of the products. To visualize this, we look at the decomposition of dinitrogen pentoxide (N2O5):

2N2O5 (g) → 4NO2 (g) + O2 (g)

So when we say "move to completion," we mean how long it takes for all possible nitrogen dioxide (NO2) and oxygen gas (O2) molecules to be formed from the reaction process.

Reaction Rates
The rate of a reaction is basically the change in quantity of a substance over the change in time. The quantity of the substance is often measured in litres, grams, moles, or moles per litre. Time, on the other hand, can be measured using any applicable unit such as seconds, minutes, hours, or even years. The unit that is the most often used for measuring reaction rates is the mole per litre-second (mol/L•s).

To monitor how fast the above reaction is going we could, for example, look at how much Dinotrogen pentoxide (N2O5) is left as a function of time. Alternatively, we could keep an eye on how much nitrogen dioxide (NO2) is formed. The stoichiometric coefficients allow us to relate these different approaches by defining the reaction rate (rt) as:

 * rt = - 1/a d[A]/d[t] = - 1/b d[B]/d[t] = + 1/c d[C]/d[t]

The above equation is used to determine the general reaction rate of a chemical reaction of the type:

 * a A + b B → c C

For the general reaction rate equation, "rt" is the general reaction rate, "A" and "B" are reactants and "a" and "b" are their respective coefficients, and "C" is the product and "c" is its coefficient. Note that even if the square brackets indicate the concentration of the substances, reaction rate can be obtained in number of moles per unit of time, litres per unit of time, or any other appropriate units. In addition, the lower case "d" represents the Greek letter delta, which, in this case, represents a change. In the above example with the decomposition of dinitrogen pentoxide, we obtain:

 * rt =-1/2 d[N2O5 (g)]/d[t] =1/4 d[NO2 (g)]/d[t]= d[O2 (g)]/d[t]

In the study of kinetics often one of the concentrations is measured over time, eg, by looking at the optical absorption by one of the species. However, it is also possbile to look at overall effects of the reaction, such as the amount of heat generated or the change in conductivity of the reaction mixture. Provided we use properly balanced equations all these can be related to the rate rt

What affects reaction rate?
So what affects reaction rates? First, we might do well to remember what is required for a chemical reaction to take place:

 * Two or more molecules must collide.
 * They must collide with enough kinetic energy to react. We associate this with the activation energy (denoted as Ea).
 * When the collision occurs, the particles must have the right orientation.

If all of the above requirements are met, an inelastic collision, one in which products will be formed, will occur. In any other case, products will not be formed since an elastic collision will take place between particles.

Increasing reaction rate
To improve the rate of a reaction, the conditions can be altered.

To improve the likelihood of a collision, you may increase the concentration, the surface area, the temperature, or the pressure if you are dealing with a reactant that is in the gaseous phase. A catalyst, which decreases the activation energy of the reaction, can also be added to increase the number of inelastic collisions per unit of time, and therefore the reaction rate.

 * An increase in the concentration of the reactants means that there are more particles present per unit volume. Statistically, an increase in the number of molecules translates into an increase in the number of collisions. If the amount of general collisions increase, the number of effective collisions will also increase. Thus, the reaction rate, that is, the number of inelastic collisions per unit time, increases.

 * Increasing the temperature of the system causes an increase in the agitation of particles. as a matter of fact, the amount of motion, the velocity of the molecules, increases. This results in an increase in kinetic energy. Since there are more particles containing an amount of energy greater than or equal to the activation energy, more particles are capable of passing the energy barrier. Statistically, this increase in the number of particles with sufficient energy to react translates into an increase in the number of particles that undergo an inelastic collision. As a result, the amount of effective collisions per unit time, the reaction rate, increases.

 * If at least one of the reactants is in the gas phase, an increase in pressure, which causes a decrease in volume, will result in an increase in the concentration of the gaseous particles. There are more molecules per unit volume, and, statistically, the number of collisions increases. If the general amount of collisions increases, the number of effective collisions also increases, and the reaction rate acquires a greater value.

 * If one of the reactants is a solid, an increase in surface area would result in a greater number of collisions between reactants. Statistically, the number of inelastic collisions per unit time increases. The rate of the reaction therefore increases. This concept explains why it is easier to ignite small pieces of wood when doing a campfire. The surface area of the small pieces of wood allows more oxygen gas molecules to collide with the fuel (wood). If a big wooden log was dropped in an unlit campfire and someone tried to set it on fire, the task would be much harder because the surface area is smaller. Another example would be the danger posed by dust particles in the air. If the concentration of dust particles is high, there is a strong risk of fire because the oxygen particles in the air are colliding with the dust, which has a great surface area.

 * If a catalyst is added to a chemical reaction, the activation energy required to trigger a reaction will be reduced. Most of the time, the addition of a catalyst causes an increase in the number of steps required to complete the reaction. Therefore, reaction intermediates make their appearance. Since the activation energy is lowered, more particles have sufficient energy to react, and the number of inelastic collisions per unit of time increase. The reaction rate, that is, the rate at which the reactants are transformed into products, increases.

Decreasing reaction rate
To decrease the rate of a chemical reaction, one can either decrease the concentration of the reactants, decrease the temperature of the system, decrease the surface area of a solid reactant, decrease the pressure if at least one of the reactants is in the gas phase, or add an inhibitor in the reaction.

title: Chemical kinetics


text:
Thermodynamics/Chemical and mechanical

Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics.

Heat is something that is observed by everyone. Warmth and coolness, combustion and oxidation - but Modern thermodynamics is concisely the understanding that heat is the result of the motion of molecules.

Thermodynamics became the unification of the concept of heat with the motion of molecules from investigations of the problem of how to increase the efficiency of early steam engines. It resulted in the understanding of statistical principles of molecules that are profound.

For the purposes of an instructive text, it will be useful to study story of efficiency in heat engines along with examples from physical chemistry in parallel.

The Heat Engine
It turns out that all engines and many other devices that do work are also heat engines. That is they can be seen as functioning by transferring heat from one place to another or generating heat while generating heat. It not only turns out that engines are the subject of thermodynamics, but also chemical reactions too.

A Simple Steam Engine
To get started, we will focus only on steam engines and see that modern thermodynamics can be seen from this example.

We'll start with a steam engine designed to pump water. You have a closed vessel of water over a flame - when the water boils, steam is produced and goes from the water vessel through a hose to a cylinder. When the steam expands into the cylinder, it will push the cylinder along from a closed to open position, from a small volume to a larger volume.

We'll put a stick on the end of the cylinder and use that to turn a wheel on a pump to pump the water. When the cylinder has gone to its furthest open position (i.e. it has expanded enough) we'll also have the wheel release the steam and push the cylinder back to its starting (or closed) position, close the valve and allow more steam to come in, we need the momentum of the wheel to close the piston. When the piston has returned to its original position, the valve moves to allow in more steam and the cycle starts again.

Looking at this arrangement, we can see that what is driving the piston is the hot steam. When the steam is hotter, the piston will drive with more force and pump more water.

The reason that this engine works is the difference in the temperature of the steam to that of the outside world. We often forget that if the temperature outside the piston were the same as inside,

Conservation of Energy
Heat is a form of energy and energy is conserved. This may seem obvious to some of us - Because heat can come from chemical reactions, like the flame from combustion, it can appear to come from nowhere.

Entropy
The spontaneous flow of heat from one body to another always goes in the same direction, from warmer to colder bodies. When we understand that heat is the result of molecular motion, we can express the flow of thermal energy as the expansion of entropy.

Zero Temperature
A profound result of the understanding of thermal energy as molecular motion is that there is a condition where there is minimal molecular motion (zero point motion), known as absolute zero. However, owing to the uncertainty principle, a molecule will never be absolutely still.

The Heat Engine
It turns out that all engines and many other devices that do work are also heat engines. That is they can be seen as functioning by transferring heat from one place to another or generating heat while generating heat. It not only turns out that engines are the subject of thermodynamics, but also chemical reactions too.

A Simple Steam Engine
To get started, we will focus only on steam engines and see that modern thermodynamics can be seen from this example.

We'll start with a steam engine designed to pump water. You have a closed vessel of water over a flame - when the water boils, steam is produced and goes from the water vessel through a hose to a cylinder. When the steam expands into the cylinder, it will push the cylinder along from a closed to open position, from a small volume to a larger volume.

We'll put a stick on the end of the cylinder and use that to turn a wheel on a pump to pump the water. When the cylinder has gone to its furthest open position (i.e. it has expanded enough) we'll also have the wheel release the steam and push the cylinder back to its starting (or closed) position, close the valve and allow more steam to come in, we need the momentum of the wheel to close the piston. When the piston has returned to its original position, the valve moves to allow in more steam and the cycle starts again.

Looking at this arrangement, we can see that what is driving the piston is the hot steam. When the steam is hotter, the piston will drive with more force and pump more water.

The reason that this engine works is the difference in the temperature of the steam to that of the outside world. We often forget that if the temperature outside the piston were the same as inside,

title: Thermodynamics/Chemical and mechanical


text:
Fundamental Organic Chemistry

Material Covered in CHEM241 Organic Chemistry I
Instructor: Jean-Claude Bradley at Drexel University

Type of content: vodcast, podcast, PDF, transcript

Electronic Configuration
Pauli Exclusion Principle: -Only 2 electrons per orbital (opposite spin) -Electrons like to be unpaired if possible

Types of bonds: covalent and ionic

Valence Periodic Table

Solving Lewis Structures

Resonance Hybrids and curved arrow formalism

Lewis, skeletal and condensed structural formulae

Molecular and empirical formulae

Acids and Bases Lowry-Bronsted Acid: PROTONS (H+) Lewis Base: Lone pair of electrons

Molecular Orbitals and Functional Groups

Atomic and Molecular Orbitals: the geometry of electron probability distribution s, p,

Hybrid orbitals sp, sp2, sp3

2 groups of electrons

linear sp

3 groups of electrons

trigonal planar (120o) sp2

4 groups of electrons

tetrahedral (109o)

sp3

Pi and Sigma bonds-the ethylene example

Rigidity of Double Bonds

Isomerism- structural isomers and stereoisomers (geometrical isomers)

Bond polarity and dipole moment Molecule Polarity: sum of dipole moments

Intermolecular Forces Dipole-Dipole interaction (e.g. CH3COCH3 acetone) Hydrogen bonding (e.g. HF, H2O) NEED F,O or N and H van der Waals forces (e.g. He, CH4)

Structure and physical properties Melting point (higher for stronger intermolecular forces) Boiling point (higher for stronger intermolecular forces) Solubility (like dissolves like)

Alkanes, Alkenes, Alkynes, Alcohols, Ethers, Aldehydes and Ketones, Carboxylic Acids Acid Chlorides, Esters, Amides, Amines

Hydrocarbons
Alkanes have a general formula of CnHn+2 (where n is a variable whole number). Alkanes have single carbon to carbon bonds and thus are saturated hydrocarbons and are the least reactive of all hydrocarbons. The boiling tempreture of alkanes increases as the number of carbon atoms increase. The first ten names of the first 10 alkanes are: Let’s count to 10: methane, ethane, propane, butane, pentane, hexane, heptane, octane, nonane, decane

Nomenclature: isopropyl, isobutyl, n-butyl, sec-butyl, t-butyl,

Primary, Secondary, Tertiary, Quaternary centers

Reactions of Alkanes 1) combustion 2) cracking 3) halogenation

Conformations of ethane, propane, butane Newman projections Steric Hindrance

Cycloalkanes Cis-trans isomerism of cycloalkanes Chair and boat configurations of cyclohexane Axial and Equatorial positions

Halogenation of alkanes
Bromination of methane Bond Dissociation Energy Homolysis and Heterolysis Transistion State (Predicting the geometry using the Hammond Postulate) Rate-limiting step

Bromination of propane Chlorination of propane (loss of selectivity) Free-radical stabilities

Carbocations/Carbanions

Chirality
R and S configurations Optical activity: dextrorotatory and levorotatory Specific rotation Racemic mixture Fisher Projection Diastereomers and Enantiomers Reactions involving chiral centers

Alkyl halides
Nomenclature

Preparation

1) Free-radical halogenation 2) Hydrohalogenation of alkenes 3) From alcohols 4) From other alkyl halides

Reactions 1) elimination 2) nuleophilic substitution

SN1 and SN2 reactions Solvent effects on nucleophilicity Walden inversion Rearrangements in SN1 reactions (hydride and methyl shifts of carbocations) E-1 and E-2 Reactions Satyzeff Rule

Alkenes
Alkenes have the general formula CnH2n (where n is a variable whole number). Alkenes contain a double carbon to carbon bond, thus making them more reactive and unsaturated. Alkenes undergo addition reactions in the presence of eg Bromine, where the double carbon to carbon bond is broken the molecule becomes an alkane. Alkenes are non-polar molecules, insoluble in water and the first four alkenes are gases, the others liquids at room tempreture. Alkenes are named similar to alkanes except the ene is added onto the end of the name eg a alkene with the formula C2H4 is called ethene. Unsaturation Nomenclature Z and E, cis and trans 8 Carbon Rule Preparation 1) Dehydrohalogenation 2) Dehalogenation 3) Dehydration of alcohols 4) Catalytic cracking of alkanes 5) Wittig synthesis

Reactions

1) elimination

2) nuleophilic substitutionSN1 and SN2 reactions

Solvent effects on nucleophilicity

Walden inversion

Rearrangements in SN1 reactions (hydride and methyl shifts of carbocations)

E-1 and E-2 Reactions

Saytzeff's Rule

Alkenes

Unsaturation

Nomenclature

Z and E, cis and trans

8 Carbon Rule

Preparation

1) Dehydrohalogenation

2) Dehalogenation

3) Dehydration of alcohols

4) Catalytic cracking of alkanes

5) Wittig synthesis

Reactions:

Electrophilic addition Markovnikov’s rule Anti-Markovnikov addition Hydration of Alkenes Anti-Markovnikov hydration by hydroboration Catalytic hydrogenation Simmons-Smith reaction Halogenation Hydrohalogenation Epoxidation Permanganate hydroxylation (cold, dilute) Permanganate (warm, concentrated) Ozonolysis OsO4 Carbenes

Alkynes
Nomenclature

Acidity of alkynes

Preparation

From dihalides From acetylides

Reactions

Hydrogenation Partial hydrogenation (Lindlar’s catalyst) Halogenation Markovnikov addition of HBr Hydration to ketones Permanganate (cold, dilute) Permanganate (warm, concentrated)

Isomers
molecules such as many larger hydrocarbons can have the same molecular formula but more than one structural formula, these are known as isomers. For example the molecular formula C4H10 has two isomers. One structual isomer forms butane while the other molecule can be rearranged to form methylpropane. The larger the molecule the more isomers that can be formed.

title: Fundamental Organic Chemistry


text:
Enzymology

Enzymology is the study of enzymes, their kinetics, structure, and function, as well as their relation to each other.

In the diagram on the right, hexokinase is displayed as an opaque surface with a pronounced open binding cleft next to an unbound substrate (top) and the same enzyme with more closed cleft that surrounds the bound substrate (bottom). The enzyme changes shape by induced fit upon substrate binding to form an enzyme-substrate complex. Hexokinase has a large induced fit motion that closes over the substrates adenosine triphosphate and xylose. Binding sites in blue, substrates in black and Mg2+ cofactor in yellow.

Biochemistry
A classification of enzymes includes
 * 1) hydrolases,
 * carbohydrases,
 * nucleases,
 * amidases,
 * purine deaminases,
 * peptidases,
 * proteinases,
 * esterases,
 * iron enzymes,
 * copper enzymes,
 * enzymes containing co-enzymes 1 and/or 2,
 * yellow enzymes

2. hydrases,

3. mutases,

4. desmolases,

5. other enzymes, and

6. polysaccharide-synthesizing enzymes.

Enzymes
Def. A substance produced by a living organism which acts as a catalyst to bring about a specific biochemical reaction. a "globular protein that catalyses a biological chemical reaction enzymes are biological catalyst that speed up the rate of a chemical reaction ss" is called an enzyme.

Theoretical enzymology
Def. a science "that studies enzymes" is called enzymology.

Electromagnetics
A "new enzymology develops around the organic liquids more favorable in the THz frequencies. ... The design of such microfluidic hioMEMS should answer to a good microfluidic and electromagnetic propagation, and should have an antiseptic character."

Hypotheses

 * 1) Enzymology through varied gene expression may hold the key to reversing deleterious gene expression.

title: Enzymology


text:
Organic chemistry/Acid–base chemistry

Acid/Base chemistry began with the Bronsted-Lowry model of acids and bases. This model states molecules containing hydrogen ions are acids, while molecules containing hydroxyl (-OH) functional groups are bases. This is not necessarily true. The recent definition of an acid and a base is based upon how the substance ionizes in water. Acids produce positively charged molecules, while bases produce negatively charged molecules. This definition allows for bases such as ammonia which does not contain an hydroxide ion. The relative strength of acids and bases is measured by their respective ion concentrations once dissolved. The product of the positive ion concentration times the negative ion concentration equals 1*10 to the -14th power. The pH is equal to -log of the positive ion concentration. The pOH is equal to the -log of the negative ion concentration. Thus, pH is measured on a scale of 0 to 14, with 7(th pH of water) as neutral. Each "step" below 7 is ten times more acidic (since it was derived from a power of ten). While rare, substances can have pH levels below 0 or above 14. However, the pH plus pOH of a substance will always equal 14.

Reactions between acids and bases always produce water and a salt. Reactions between acids and metal always produce a salt and hydrogen gas.

title: Organic chemistry/Acid–base chemistry


text:
Organic chemistry/Reductions

Reduction is the loss of oxygen from a molecule or the gaining of one or more electrons. A reduction reaction is seen from the point of view of the molecule being reduced, as when one molecule gets reduced another gets oxidised. The full reaction is known as a Redox reaction.

In the case of Organic Chemistry it is usually the case of the gaining/loss of Oxygen/Hydrogen

In Inorganic Chemistry the term refers to the change in oxidation state of the metal center.

title: Organic chemistry/Reductions


text:
Organic chemistry/Oxidations

Oxidation is a process where a substance:

a) loses one or more electrons;

or

b) gains oxygen atom/s;

or

c) loses hydrogen atom/s;

or

d) gains an increase in its oxidation number.

For example:

C + O2 ->CO2

Here C ie carbon gets oxidised while oxygen is reduced. This is simple combustion of carbon.

title: Organic chemistry/Oxidations


text:
Portal talk:Analytical chemistry

Transwiki from Wikibooks
I've transwikied the old pages from Wikibooks, and the index page can be found at School:Chemistry/Import.--digital_metalk 02:19, 20 August 2006 (UTC)

 * Thanks :-) --HappyCamper 02:21, 20 August 2006 (UTC)

School:Chemistry
There is now School:Chemistry as it was developed at Wikibooks. The Topic:Chemistry page should be re-named (and moved to the new page) as a department within the School of Chemistry, maybe something like Topic:Analytical chemistry. --JWSchmidt 03:22, 26 August 2006 (UTC)

 * Okay, great! --HappyCamper 00:30, 27 August 2006 (UTC)
 * Move complete to Topic:Analytical Chemistry. --JWSchmidt 09:36, 4 September 2006 (UTC)

As I posted under the School:Chemistry page, I will be taking Organic and Analytical Chemistry courses this upcoming semester. I would like to contribute, and it seems like much work needs to be done. What materials do we already have available? HallAtHarding (discuss • contribs) 15:11, 6 August 2013 (UTC)

how can you learn analytical chemistry theoretically?
what do you expect to have here? how can you learn analytical chemistry theoretically?

title: Portal talk:Analytical chemistry


text:
School talk:Project management

Slash and burn
I am a construction worker /SLASH/ Engineer |slash| a lot of other things. I have felt the burn of being fired only once, but that was in an unrelated discipline, altogether. So, suffice it to say, I know successful Project Management when I see it. I have been an electrical contractor for many years and I think that in the context of construction, particularly in a capitalistic environment should be a sensitive study, tempered with Experience. 19:13, 8 January 2007 (UTC)

title: School talk:Project management


text:
School:Engineering and Technology/Engineer-In-Training Review

Return to b:Wikiversity:School of Engineering

Welcome!

The Wikiversity is just emerging. I propose that we review the necessary material by helping get various general and specific engineering curriculum material compiled, tutoring, mentoring, and (of course) some studying and evaulation of existing materials.

Simultaneously we can draft a core critical minimum of review material with links to the more exhaustive materials used by the current participants pursuing initial studies of rudimentary and advanced material. This will allow each of us to individually address our weaknesses while all of us benefit from our aggregate strengths.

General Engineering Fundamental Core Classes List b:Wikiversity:School of Engineering

General U.S. Fundamentals Exam

Oregon defers/refers to the National Board of Engineering Examiners

Specific Disciplines or Specialties According to each U.S. State P.E. exams.

 * Oregon
 * Systems Engineering - I will contact the state to get the specific guidance available on the current state of the testing or associated state or Federal exams and licenses that are applicable according to the Oregon Engineering Board of Examiners. Lazyquasar 03:21, 28 November 2005 (UTC)
 * Online starting point.
 * Ouch! Looks like HP41CV may be out due to primitive word processing capabilities. May have to spring for a straight sliderule with RPN and get started practicing with it.  I just hope one on approved list is RPN.


text: Category:Biology

title: Category:Biology


text:
User:Deon555

Soft Redirect: this page can be found at w:User:Deon555 until this user has established a good User Page :)

title: User:Deon555


text:
User talk:Deon555

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional editing help.

You will find more resources at the Community Portal. If you want to ask a question, visit the Study help desk, the Colloquium, IRC channel or ask me personally on my talk page.

Good luck!--Deon555 00:07, 22 August 2006 (UTC)

custodianship mentoring
I like the idea that custodianship should be "no big deal".....it should be easy to get and easy to have taken away if abused. Until Wikiversity has a clear policy for termination of probationary custodians, I need to stay with the minimum requirement for custodianship, that the candidate be "a trusted member of the community". "I think that custodian candidates should demonstrate (by good editing) their commitment to the Wikiversity project before expecting to become a custodian." I cannot be your mentor until you build up a record of useful edits here at Wikiversity. --JWSchmidt 00:44, 22 August 2006 (UTC)

 * "hopefully you'll be able to mentor me in the future" <-- I'm sure it will work out that way. --JWSchmidt 02:48, 22 August 2006 (UTC)

title: User talk:Deon555


text:
User:Ryan~enwikiversity

When I first saw this page it seemed sterile and empty (and still is), but I hope to help by any means I can to make this an extremely useful site. Its premise is unlike that of which I have ever seen before, and hope that it thrives as it very well should.

title: User:Ryan~enwikiversity


text:
Human Biology

Biology is the study of life. The Wikiversity Division of Human Biology is specifically concerned with human biology. This division will guide you through your study of how and why the human body works the way it does.

Lessons

 * The Human Body: Most likely this will be a large part of the biology department. It will have many subsections and numerous articles for each one.

Resources

 * whaaz provides updates on various topics related to biomedical science. You can also add your own articles.

title: Human Biology


text:
User talk:Ryan~enwikiversity

Hello and welcome to Wikiversity!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional editing help.

You will find more resources at the Community Portal. If you want to ask a question, visit the Study help desk, the Colloquium, IRC channel or ask me personally on my talk page.

Good luck! Messedrocker 04:51, 20 August 2006 (UTC)

I would like to cordially invite you to join me at the School of Zoology as it grows. Hope to see you there! =D --AmandaEP 18:47, 7 December 2007 (UTC)

altered pages
I changes some of the biology pages in order to place them within School:Biology. --JWSchmidt 13:33, 28 August 2006 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Ryan. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Ryan~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:42, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:21, 19 April 2015 (UTC)

title: User talk:Ryan~enwikiversity


text:
School:Mathematics

Welcome to the School of Mathematics! FACULTY OF SCIENCES F ACULTY OF P HYSICAL S CIENCES  · F ACULTY OF L IFE S CIENCES  · F ACULTY OF E NGINEERING AND  T ECHNOLOGY  ·  F ACULTY OF M ATHEMATICS Biology · Chemistry · Computer Science ·Economics · Mathematics· Physics and Astronomy ·

Since you're here, you either are someone wishing to share your knowledge of Mathematics, or you are someone who wishes to gain knowledge about Mathematics. If you are the first kind of person, have a look around, and see how you can contribute. If you are of the second kind, read on!

Mathematics has many facets; though it has a wealth of applications, Mathematics is also a science, and an art, in its own right. Like other sciences, Mathematics is useful, but, just like other forms of art, Mathematics is beautiful, in its own unique way. You might not see this beauty at first, but the main goal of the Wikiversity School of Mathematics is to let you see this beauty, through inquiry and learning. To achieve this goal, we want to inspire you, since inspiration is essential to learning, discovery, and ultimately, seeing the beauty of Mathematics. A little bit of inspiration can put the beauty of Mathematics, and all its facets, before your eyes.

The School of Mathematics is a work in progress. We are trying to organize our material into a logical order, create new material, and revise existing material. Although we try to keep clarity in mind, if any of the material is confusing, you don't know where to start, or you have other questions, do not hesitate to pose your question at our help desk. There is no such thing as a "dumb question"; learning is driven by questions!

The School of Mathematics wishes you a very warm welcome. We hope that you will benefit from what we have to offer, and we hope that we will benefit from what you have to offer, either now or in the future.

Divisions and departments
Divisions and Departments of the School exist on pages in "portal" name space. Start the name of departments with the "Portal:" prefix; departments reside in the Portal: namespace. Departments and divisions link to learning materials and learning projects. Divisions can link subdivisions or to departments. For more information on schools, divisions and departments look at the Naming Conventions.

To add additional Divisions or Departments within the School of Mathematics, edit the list of "Portal:" namespaces on the MathDeps Template.

Mathematics curriculum
This Wikiversity School of Mathematics project aims to create a structured set of links to learning material and test questions for the mathematics curriculum. To start, the recently released Australian national senior secondary school curriculum is being used as a guide. It is possible to create a similar structure based on the curriculum of alternative educational systems, but copy some of the same links and material identified below. If you'd like to do this, please create another heading in this section. Alternatively, please feel free to contribute to the project based on the Australian structure. This structure is fairly generic.

Australian national senior secondary school mathematics curriculum
These headings will provide links to pages detailing the senior secondary school mathematics curriculum. It will be used to identify material on Wikiversity and other Wikimedia sites that might be useful to students and their supporters. It will also help show the links between different areas of the curriculum and where studying mathematics might take them in the future; in other words, some possible answers to the eternal question, "why should I learn this?" and help show students the doors that will open to them by learning to see the world mathematically. The recently released Australian national senior secondary school mathematics curriculum will be used as a guide for this Wikiversity School of Mathematics project. (This material is based on the curriculum developed by the Australian Curriculum, Assessment and Reporting Authority (ACARA), which states its curriculum material can be downloaded, copied, printed and communicated for personal or non-commercial purposes, including educational or organisational use under a Creative Commons licence: copyright information)

 * Essential mathematics
 * General mathematics
 * Mathematical methods
 * Specialist mathematics

School news and current events

 * 31 December 2018 - Convergence acceleration by the Ford-Sidi W(m) algorithm - announced on Main Page News!
 * 30 December 2018 - Speak Math Now!/Week 1: Introduction To Algebra - announced on Main Page News!
 * 19 December 2018 - Vectors and coordinates - announced on Main Page News!
 * 30 September 2018 - Divergence (Gauss-Ostrogradsky) theorem - announced on Main Page News!
 * 2 June 2018 - WikiJournal of Science/Spaces in mathematics - announced on Main Page News!
 * 20 January 2018 - Mathematical Properties - announced on Main Page News!
 * 11 January 2018 - Boolean domain - announced on Main Page News!
 * 6 November 2017 - Legendre differential equation - announced on Main Page News!
 * 31 August 2017 - Minimal negation operator - announced on Main Page News!
 * 15 July 2017 - Line (Geometry) - announced on Main Page News!
 * 1 July 2017 - Unknown coordinate systems - announced on Main Page News!
 * 16 June 2017 - Multiple linear regression - announced on Main Page News!
 * 31 May 2017 - Full octahedral group - announced on Main Page News!
 * 26 January 2017 - Quadratic Equation - announced on Main Page News!
 * 21 January 2017 - Inversion (discrete mathematics) - announced on Main Page News!
 * 19 January 2017 - Permutation notation - announced on Main Page News!
 * January 2014 - Mathematical astronomy - announced on Main Page News!
 * March 2008 - 140-year-old math problem solved by researcher
 * April 2007 - E8 mapped...
 * 20 August 2006 - School founded!

Study guides
Not sure where to start? Consult the following guides to help you make a study plan and determine which prerequisites you might be missing.
 * Course guide
 * Facultative courses

Course categories

 * Applied Mathematics (mathematical methods, mathematical physics)
 * Pure Mathematics (foundations, algebra, analysis, calculus, discrete math)
 * Probability and Statistics
 * Math contest preparation
 * All Courses (Course Catalog)
 * Nonkilling Mathematics--would fit better under Ethics and Philosophy

Lectures

 * MacLaurin series
 * Mathematics

Video courses

 * Stillwater AP Calculus Tutorial Videos
 * Open Course Ware by MIT contains lectures for most of the topics in College level mathematics
 * NPTEL's Basic courses and Mathematics includes many lectures on subjects in mathematics. Recommended for Engineering mathematics
 * Harvard University Extension School offers lectures in many subjects. Recommended for Abstract Algebra.
 * Khan Academy which has a youtube channel with many easy to understand math videos from arithmetics to calculus and linear algebra. Recommended for School level mathematics
 * Chycho, has videos on Youtube organized by kpsssubject. Author uses big chalk and street walls for presentation of material.
 * MathTV's Youtube channel
 * MathTV's website with the material organized by subject. They say they may start charging, but the videos will still be accessible on Youtube.
 * Is all about Math video podcast with animations explaining math.
 * Patrick Just Math Tutorials patrickjmt.com is a math only website with extensive free math content; he also has a youtube channel, 'patrickjmt.'
 * the Technion YouTube playlist channel contains lectures for many university level subjects, mostly in Hebrew.

Free Software

 * GNU Octave - A computational program similar to (and mostly compatible with) MATLAB
 * SciPy - A Python library for mathematical and scientific computing
 * Maxima - A computer algebra system
 * SINGULAR - A computer algebra system
 * GAP - A tool for computational group theory
 * R - A programming language designed for statistical computing
 * FreeMat - An open source Matlab clone
 * SAGE - A packaging of many of the above software tools and more
 * Pari/GP - "a computer algebra system with the main aim of facilitating number theory computations" (from Wikipedia)
 * Mathics Mathics is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions.
 * See a full list along with some commercial tools at our mathematics software page.

Other

 * Other Free Learning Resources/Mathematics

Active participants
The histories of Wikiversity pages indicate who are the active participants (listed below). If you are an active participant in this school, you can list your name here (this can help small schools grow and the participants communicate better; for large schools it is not needed).

 * Since 7 January 2012 with Mathematical astronomy --Marshallsumter (discuss • contribs) 11:27, 10 May 2019 (UTC)

Inactive participants

 * Parth Kohli (Set Theory, Calculus, Algebra, Trigonometry, Logic, Applied Mathematics)
 * TortoiseDream (Logic, Set Theory, Mathematical Physics)
 * Tastymangojuice (Computer Science)
 * ehremo
 * Deltinu
 * EulerGamma
 * Ravi12346
 * Lucas Gallindo
 * Pgbridge2000 (Cryptography)
 * Tachyon01 (Pure Mathematics)
 * fidocancan (pre-uni teacher)
 * Mo Anabre
 * sutton
 * Drini
 * Ananth nag m
 * TeapotScar (Calculus, Number Theory, Topology)
 * pbran7
 * Juan (Topology, Algebra, Geometry and Analysis)
 * Ivanne (I just want to learn man)

 * King Bee (graduate student in pure mathematics)
 * Verin Sedai (Algebra, Combinatorics, basic number theory)
 * haresh kumar(analytic geometry,calculus)
 * A.K.Karthikeyan(True knowledge lies in knowing you know nothing)
 * Tlep (Algebra)
 * Bigyan Shrestha (Mathematical Statistics)
 * Rogerh
 * Madhur Sarin (Number system,Geometry,Calculus )
 * AFriedman (Computer Science, Biology)
 * User:fibonacci101 (Geometry, number theory, set theory)
 * User:mathclubowner
 * Helloworld00
 * graie
 * mynameinc (Algebra, Trigonometry, Differential Calculus)
 * Comrade1986 (Mathematics)
 * user:WendyB (Mathematics student)
 * user:Alchemy heels I (Mathematics student)
 * John Michael Pinson I (Numerology, Mathematics student)
 * Tarun-Science (I;m a 15-year-old intersted in Physics, Mathematics and Chemistry..good in geometry and algebra)

International relations

 * it:Wikiversità - Facoltà di Matematica
 * |Wikiversidade - Ciências Exatas e da Terra

title: School:Mathematics


text:
School talk:Mathematics

Two different pages were created for "School of mathematics". The original page for the School of mathematics that was developed at Wikibooks was imported to School of Mathematics. The material from that page was pasted into School:Mathematics. --JWSchmidt 01:04, 26 August 2006 (UTC)

Maybe it should be the "School Of Infomatics" because of it's integration with Computer Science

Disorganized Content
All of the content in the School of Mathematics seems to be very disorganized. Articles on the same topic are distributed in many places. Are there any plans for the structure of the content? I am unsure where to contribute lectures. --Pps 16:57, 30 July 2008 (UTC)

 * I agree. I am taking inspiration for my projects from Introduction to Swedish. This is a fine example of project design that could suit the mathematical department well. Donek (talk) - Go raibh mile maith agaibh 19:13, 21 August 2008 (UTC)

 * Second. I think everyone needs to look at this: Topic:Electrical_engineering. It appears to be the most well organized topic page I have found. Anyone willing to tackle that challenge.

 * Wow. School:Electrical_engineering is brilliantly organized. There should be a standard, organized layout for all School: pages. It is confusing for others if each page is not organized in mostly the same way. Charcoal (talk) 00:17, 24 May 2010 (UTC)

It looks like a lot of the content here is under the topic namespace when it wouldn't really qualify as a department (see Topics). Using School:Engineering as a model, I propose we structure topics roughly as follows:

Elementary Mathematics
 * Primary School
 * High School/College

Applied Mathematics
 * Actuarial Science
 * Applied Analysis and Differential Equations
 * Discrete Mathematics
 * Game Theory
 * Numerical Analysis
 * Mathematical Physics
 * Probability
 * Statistics

Pure Mathematics
 * Algebra
 * Algebraic Geometry
 * Abstract Analysis
 * Category Theory (Possibly merge with Algebra?)
 * Graph Theory
 * Mathematical Logic & Foundations
 * Number Theory
 * Philosophy of Mathematics
 * Topology

The topics that we have now would then be moved to courses in their respective departments since the individual course topics don't seem to have enough content to warrant their own departments right now. Maybe once we have more than 2-3 courses on e.g. group theory, sub-departments can be made, but for now it just seems cluttered with empty departments.

We could also probably borrow some of the page layout from School:Engineering, since it seems to be organized very well. I'd be willing to do the restructuring if this sounds good to people, but I don't really know how to move pages, or even if I have the necessary permissions.

Finally, we have a large list of contributors on the front page. I understand there's some way to see if they're all still active or not, although I don't know how to do that. It would probably be beneficial to move most/all of the list to a separate page. Any thoughts? Ndriscoll 09:14, 7 July 2011 (UTC)

Algebraic Notation & keeping articles understandable
This is a great idea! However, i think that it would be good to start with a page explaining algebraic notation right from the basics through to advanced notation. The articles also need to remain understandable for their target audience for example if an article is aimed at high-school students, it needs to be understandable by them. Although articles shouldn't be 'dumbed-down' but just expanded to explain the basics before developing the more advanced topics. 217.44.174.151 19:54, 5 December 2006 (UTC)

Unification of Information
Would it be possible to unify some of the parts of this School to reduce the workload of maintaining separate, but similar sections? For example, it might be useful to have all reference material for a particular subject on the same page. I suggest this for two reasons. First, maintaining two similar but separate pages is difficult, and second, I think unifying some material would make it easier for newcomers to find what they are looking for. Ideas? Comments? Deltinu 05:18, 2 September 2006 (UTC)

Curricula
One thing we need to develop here is a set of mathematics curricula for grades K–12 (i.e., what students should know in what grade). I've gone looking for this information online myself from time to time and never found a satisfactory list that I didn't have to pay for first. (Of course, it goes without saying that we should not simply copy any lists found at other websites, free or not.) To this end, I've begun the page Mathematics curriculum (with the plural Mathematics curricula as a redirect). - dcljr 23:52, 5 September 2006 (UTC)

The UK Gov. publishes it's school curricula online here: http://www.nc.uk.net/webdav/harmonise?Page/@id=6004&Subject/@id=22 These could be used as a model. Smockdotcom 21:05, 2 October 2006 (UTC)

About the Statistics and Probability Courses
Who is contributing to the advanced undergraduate/graduate courses on this subject? The undergraduate course on statistics shouldn't be in the Department of Statistics page? --Lucas Gallindo 03:15, 11 September 2006 (UTC)

Mathematics Userbox
Here's a user box that you might interested in:

Use of 'Math'
This isn't used in the UK, 'Maths' is used instead of mathematics. Better to use mathematics all round I think. Smockdotcom 21:17, 2 October 2006 (UTC)

Why are combinatorics and optimisation put together?
Please forgive my ignorance. I think they are different topics with some overlapping.Hillgentleman|User talk:hillgentleman 10:37, 24 November 2006 (UTC)
 * They are not always put together. When they are put together it would be, because as you mentioned, there is significant overlapping, and there is enough time in a course to cover both.  Combinatorial optimisation is an actual sub-subdicipline of mathematics that is right at the boundry between Discrete Maths and Theoretical Computer Science.

Main page picture
Would it be possible to have the picture at the top of the School of Mathematics main page cycle through a selection of several different pictures? The main page for the whole of Wikiversity seems to have this feature. It might be good if we could implement this for our school's main page.

Deltinu 05:27, 26 December 2006 (UTC)

{| align=right padding=0 cellspacing=0 width=32% style="background:none"

That is how it is done on the right bar of the main page (http://en.wikiversity.org/wiki/Wikiversity:Main_Page/Communications_and_community).

 * Thanks :-) Deltinu 07:04, 26 December 2006 (UTC)

Eculid's Elements...
Have started an effort to copy a 1896 version (now in the Public Domain) into WikiSource here : http://en.wikisource.org/wiki/The_Elements_of_Euclid

You may want to take a look :-) ShakespeareFan00 20:23, 20 March 2007 (UTC)

Getting the Algebra page up to snuff
In case you haven't seen it, there was an article about how incomplete the college algebra section of wikiversity is. If this were wikipedia, this course would be full fixed and up and running. Of course this is wikiversity, where ideas lingure and aren't acted on for months at a time. Algebra work is spread over a miread of pages, but I'm going to focus on getting College Algebra a good go first, since it is the one that people reading that article will be reading. Hopefully others can help, but I'm going to see what I can do on my own first. Hopefully it will be more than what has been done in the last half year.--Rayc 20:56, 31 July 2007 (UTC)

I found the volume of algebra pages and the general outline of the math portal to be so confusing that I felt it necessary to flesh out the new algebra department with organization. It's a constant battle of content development versus organization until we get a steady state. Please lets everyone categorize everything as obviously as possible sos we can find our ways around in the dark. - gustable

old talk page rescued
Hi, there was still comments from the old page available at Talk:Wikiversity:School of Mathematics. Before deleting that page, the content is saved below !!

activity
I am building activity based content targetting US Middle and HS Math students. The primary activity builds on work done relating mathematics and origami with connections to physics, chemistry and biology. I currently teach in a small school in Oracle, AZ. This is an emerging area with opportunities for collaboration, linking and sharing.

Peter Edwards, Tucson AZ

I'll help. However, we need to have lesson plans and a true syllabus. Look in my profile for the book/course i was trying to create. That's somewhat of an image of how I would like to organize a school of mathematics into. Starting with Basic Mathematics and moving up into Calculus. The thing that differs a course from a book is that the instructor knows that some books suck and so he has to guide his students through the various books. I find flaws in many of the wikibooks and so I try adjusting them and linking them. I found that the PEMDAS section wasn't actually the greatest, mainly because they show exponents using PEMDAS rather than teaching exponenets. Thus i gave a see also link. Perhaps we should create a member book. I've always had an interest in such thing as a member book. An log of things that still need to be done to complete a course. What part editors are working on and what part authors are working on. Whatn parts they need resources in. Quiz material, diagrams, so forth. --Cyberman 02:11, 20 Feb 2005 (UTC)

Courses
I have started work on a course based closely on the first semester of my university's mathematics course. I have also started with creating categories for other courses. Help would be happily accepted. Also, feedback would be appreciated. You can contact me by my talk page or by emailing me at my email.

--Jimmy 02:00, 8 Aug 2004 (UTC)

We already have a Mathematics bookshelf. Shouldn't these links go on that page, so readers can find the contents more easily? Carandol 12:40, 8 Aug 2004 (UTC)

The difference is that this is a 'course' not a book. People don't look here for information, they use this as a syllabus for whatever reasons they might have. So I don't really think it should just be another book on the bookshelf. Of course, within the course(s), it would often be referred to the bookshelf for extra information, questions etc.

--Jimmy 14:24, 8 Aug 2004 (UTC)

Any course that is more than just a list of topics is effectively a book.

Thus many textbooks are just printed versions of successful courses, and many lecture courses oral presentations of a particular textbook. The difference is minimal, the overlap considerable.

A syllabus that said, say, 'Lesson 1, Proof by induction; Lesson 2, Summation of standard series; ...' and no more wouldn't be a book, but that does not seem to be quite what you are planning. Carandol 14:11, 9 Aug 2004 (UTC)

Its still in work... it takes time you know... Jimmy

Division by topic vs. by school level
Whouldnt it be better if there was "stages" of mathematics divided in topics rather than "high school" and primary school mathematics? Becouse im not really sure what those deal with becouse im not from the us. :/

I prefectly agree with your idea. It is kind of stupid to say "high school math", "primary school math". For example, calculus is high school subject for some but university math subject for the others.-Wshun 15:21, 4 May 2005 (UTC)

 * I also agree, but what other method would you suggest? Just list the topics in order of difficulty?  I mean, math is mostly linear until you get to 2nd/3rd year University level, so is that what you're thinking--just list the topics in order from most elementary to most advanced?  Gandalfxviv 19:30, 26 February 2008 (UTC)

 * The stages idea is perfect, but don't forget, multiple stages can be placed in each of the three academic levels, i.e. primary, secondary, tertiary. Donek (talk) - Go raibh mile maith agaibh 19:16, 21 August 2008 (UTC)

Actual Courses
Why are they all... based on types of equations and stuff. WHy don't we make them based on actual mathmatics courses that can be taken through high school and college like...

Pre Algebra Algebra Geometry Algebra II Pre Calculus Calculus Calculus II Calculus III Statistics and so on...

Why make it so confusing? We should make it in a way where people can actually understand what it is their learning based on the cource title. --Dinero 02:15, 19 Apr 2005 (UTC)

Agree! Indeed we can make it even better then the actual courses. Connection among different topics should be made more efficient than our real life courses. -Wshun 14:35, 4 May 2005 (UTC)

Wikiversity is a noble but perhaps misguided effort. the learners will tend to be self leaners who will not want they're hand held the entire way. Perhaps wikiversity shoudl be structure on wikibooks so that the current textbooks we have supply as the course material.

Translation
I need help on translating a course in mathematics. Please follow the link for details. Dmitri83 11:55, 2 May 2005 (UTC)

Dependecy Tree Nature
Mathematics has a much stronger "dependency tree nature" than most subjects, understanding of a previous subject is vital to understanding the current subject. A common problem in university math courses is that students do not fully understand/remember some previous concept or were never taught some fundementals; either because it was too hard, and the teacher taught by rote memorization* or never really explain the reasoning of mathematics.

Because of this, I suggest authors of books and syllabues would create conceptual backlinks to dependent material in their work. So for example, if you have sentance that has the word "set" in it, you would backlink to a section of a book on set theory, that section would contain well integrated backlinks to other fundementals (which might eventually go into number theory and the philosophy/history of mathematics). So for the person who asks why, they would be quickly redirected to their answers. Reading my textbook right now, if it had that kind of comprihensive hyperlinked backtracking, I would be soo more productive.

 * I think this is a good idea. However, I think we also need to keep in mind, that redundancy can be useful. For instance, if we have a book on set theory, it still might be useful to give a summary of what sets are in another book. I think having the same thing written in different ways can be helpful for the reader.

Also, when going through examples and proofs, manipulations tend to be shortened and some details are skipped assuming you already remember perfectly the previous subject. So for example: $$\frac{k(k+1)+2(k+1)}{2}$$ is just reduced to in one step $$\frac{(k+1)(k+2)}{2}$$, vs. showing $$\frac{k(k+1)+2(k+1)}{2} = \frac{k^2+k+2k+2}{2} = \frac{k^2+3k+2}{2}{2} = \frac{(k+1)(k+2)}{2}$$ (that could of also had a table to the right showing the various backlinked laws being used).

That could get tedious quick for someone who does know perfectly how it works. So in addition to actually showing your work, you can have "hiding" options (like a directory tree almost) which hide the simpiler details for you.

You could even automate some of this by computer.

 * (My highschool teacher said something approximate to this: "I'm not going to explain the why of logarithms, it's just faster to memorize this 7 x 5 table of formulas and be done with it and plus I don't really understand it myself.")

 * --MahyarMcDonald 07:19, 6 November 2005 (UTC)

Calculus course
Is it alright for me to start a calculus course on here?

Oh good heavens Please do!! -user:gustable

No courses in Differential Equations?
I came here to brush up a bit on DE since I'm taking DE 2 next semester and it's been 2 years since I took DE 1. However, there seems to be very little on the topic of differential equations here and no DE course at all. DE covers important material, and most science and engineering programs require at least one or two courses in differential equations (on top of basic and intermediate calculus). DE is certainly a lot more important, and is far more widely used than things like set theory or number theory (which both already have courses). So why are there no DE courses yet?Uniqueuponhim 13:13, 21 October 2007 (UTC)

Topology
Are there enough people interested in forming a sort of topology team? I noticed someone started the Topology topic and I wrote the first lesson for it, just wondering if there were any other people that wanted to help out with it, since it's still in such a beginning stage. Gandalfxviv 19:34, 26 February 2008 (UTC)

Fractions and math basics
I just looked through the fractions section here at Wikiversity and it could use some work. Fortunately, we don't need to write anything, we can just borrow a lot of the necessary material from Wikibooks' Applied Math Basics; the fractions section there is much more complete and in-depth. --71.112.145.203 07:12, 8 June 2008 (UTC)

Collaboration
Would anyone like to help with teaching on Medical Statistics? Go raibh mile maith agaibh 23:50, 17 June 2008 (UTC)

Effective Teaching
I just recently found this particular wing of the wikimunity and upon poking around a little I can see that it is still very much in its infancy as there isn't much much standard material above calculus like ODEs, PDEs, fourier series, complex analysis and other thing that non-mathematicians like to use. Now, I'm not complaining, this is a good thing from my perspective because it means I can help the comunity more. Anyway, what I want to say is that I believe that one of the major issues with how math is tout is that almost all text and many teachers do not care to show students all the steps involved with the problem. I understand that this is a difficult thing to tag down, when you are teaching a calculus class you should not have to tell people every time you use addition. In the interest of time teacher and texts alike choose to leave out menial steps and operations along that way and students are expected to keep up. I don't mean to criticize these teachers, however, this is the overwhelming complaint from the average student. I do want to criticize most text as they have no excuse and often times leave out more than a lecture would when attempting to explain advanced concepts. Now, as I said before, when teaching a calculus class you shouldn't have to tell people every time you use addition, however, the problem is that much more complicated are often left out and with no consistency. Every teacher and text makes different assumptions as to what students are expected to take for granted. I would like to propose that the School of Math here dose something to help this. Every lecture should establish a list of assumption that are made concerning methods and steps used that lecture. The words: "by inspection", "obviously", "by algebra" (or any other relatively lower level math), "it can be seen", "it can be shown", and (I have actually seen this before!) "as any small child can see" should never be used in any explanation of anything on the site. I know some people call this hand holding and spoon feeding and what not, but you know what, some people need that, there are many times it would have helped me. It's far easier to glaze over a step you didn't need to see than it is to be stuck trying to figure out what happened in the whitespace between two lines of an explanation. Again, I think the most practical way to do this is to state exactly what type of steps you intend to skip at the beginning of a lecture and stick with it. It should also be particularly easy for readers to ask for such information when they are studying lectures. Anywany, thanks for reading, please tell me what you think. Smitty985 05:42, 10 November 2008 (UTC)Smitty958

Complexity Theory
Technically, Complexity Theory (Topic:Complexity_theory) is Computer Science, but Computer Science is categorised under engineering, which Complexity theory is not. Would it be possible for the topic to be included in both? This is a moot point and concerns itself more with the semantics of the term ‘Computer Science,’ but I think it is important. Many Mathematicians work in the field of Complexity Theory, as do many Computer Scientists, so I would consider it to be an ‘Interdisiplinary Study.’

Does this count as a formal request for the inclusion of the Institute of Complexity Theory in the School of Mathematics?

― Kinkydarkbird 09:38, 7 January 2009 (UTC)

Emptying out Active Participants
If there are no objections I was planning to empty out the active participant list a bit, just so those of us still around who have a better idea of who they can talk to. My criteria will be the most recent edit, if someone hasn't contributed in a year or so I think it should be safe to remove them for the active participants list. Thenub314 13:03, 29 July 2010 (UTC)

Transferring content from Wikipedia
Hello. I am a Wikipedia editor new to Wikiversity. Is Example of a non-associative algebra something right here, e.g. in topic: Higher algebra? It is definitely not an encyclopedic topic (at least as “Example”, in singular) and the content now is essentially superseded with Composition algebra. There will be no harm to Wikipedia to remove the problematic “article”, but possibly this project is interested in an already written and formatted content of such kind. Incnis Mrsi (discuss • contribs) 08:25, 18 May 2013 (UTC)

Identify coverage of the Common Core mathematics curriculum
I suggest that as courses are added those that intend to meet the goals of the common core curriculum be noted. See: Common_Core_State_Standards_Initiative and also: http://www.corestandards.org/Math/ In addition, it may be useful to explicitly state that one goal of the School of Mathematics is to eventually include learning resources that taken together meet the full curriculum requirements. Thanks! --Lbeaumont (discuss • contribs) 17:04, 20 March 2016 (UTC)

Organization of content
The content needs to be more organized in a more precise way at: School of mathematics. Rayn777s (discuss • contribs) 13:13, 24 July 2020 (UTC)

 * Be bold. If you have a vision for organizing the content, please do so. -- Dave Braunschweig (discuss • contribs) 15:17, 25 July 2020 (UTC)

Abi na Zie afeo (discuss • contribs) 19:19, 9 December 2021 (UTC)

Content expansion
Hello, the university wiki should expand its contents through the resources of the sister project, i.e. wiki book, wiki source and wikipedia.

You can also write sample questions so that people can improve their knowledge by solving them. AHEJJWILEMAMALIDGED (discuss • contribs) 07:53, 20 October 2022 (UTC)

title: School talk:Mathematics