Komnen

Math and Chemistry

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Can someone give me any ide for any study which includes Mathematic and Chemistry in one study?

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At what level?

 

Generally, I would say that there is almost no mathematics in chemistry apart from basic numeracy. There are exceptions like quantum chemistry, molecular dynamics and similar. And even then, the level of mathematics will depend on personal preferences to a large extent.

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Whilst I think ajb's comments were a bit harsh, he also asked a good question

 

At what level?

 

There is the Cambridge University Physical Science Tripos - Maths, Chemistry and Physics

 

You might also look at chemical engineering, which includes more maths than pure chemistry

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I am a Math student at my last year of study(4th) and i have all my roomfriends students of Chemistry and I like a loot to have a study for Analitic Chemistry ( they have a lot of math problem to do in this studies) to find a fast way for them to solve they problems .

But before I will start to do this , i would like to find more ideas for this stuff.

 

 

ps . Chemistry engineering

Edited by Komnen

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So you are thinking of an MSc or PhD in `mathematical chemistry'?




Whilst I think ajb's comments were a bit harsh


I accept that.

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A good knowledge of statistics is essential in experimental chemistry, particularly analytical chemistry.

 

4th year of what?

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MSc will be good for me .

 

I am in 4th year of study of Mathematic in Scienc Faculty of University of Prishtina , Kosovo.

 

Dont know for other countryes but we have a poor library in our language for analytical chemistry , so a study of this will be good for my University .

 

So no idea from you ? :P

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Chemistry is far from my interests - however I am sure you can find MSc programmes on mathematics and chemistry. You have have to leave Kosovo though.

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How to say , I am someone who is so low in Chemistry knows, and I am asking you if there is any part of Chemistry that I can put my Math know there to make a study , with help of my chemistry friends.

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Ask your friends to explain chemical kinetics (rates of reactions) to you.

 

Particularly in respect of catalysis and surface chemistry.

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Can someone give me any ide for any study which includes Mathematic and Chemistry in one study?

See my signature video.

It's all chemistry, mathematics, and programming.. :)

 

You could try making simulation of reaction between two (or more) substances.

At the beginning you have 100% of 1st let's say HCl,

and 100% of 2nd let's say NaOH,

entered by user as mol (* Na = absolute number of molecules).

Then as reaction goes calculate probability of finding H+ with OH- (and ending up H2O) and probability of finding Na+ with Cl- (these remain ions in solution),

make equation (with time as argument),

how they join (absolute quantity/moles/mass/volume).

It could be with 3D visualization of the whole process.

With/without stirring/heating. With custom made containers various sizes, various shapes.

 

You could end up with something like "particle physics simulation" but for chemistry..

https://www.youtube.com/watch?v=x8Fo2slT2WA

 

Edited by Sensei

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There is an entire discipline called mathematical chemistry. I think it's mostly to do with topology and graph theory. Perhaps look into that?

 

Sensei also touches on the first area that I thought of, though his explanation / example is a bit oversimplified. Computational chemistry - which deals with a lot of modelling of various systems - requires a great deal of math and programming skills, which you might find to be in your area of interest. It encompasses a pretty wide range of sub areas, so you may wish to look up the discipline yourself. Kinetics and other aspects of physical chemistry are good also, but these areas have huge wet lab components and a solid understanding of practical techniques. In either case, you will also need some understanding of chemistry. Not having this would put you at a disadvantage, since you wouldn't fully understand the systems you're working with. I do not believe that mathematical chemistry would rely on such a contingent.

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In the simplest brute-force algorithm of particle simulation,

there is array of particles (quantity entered by user).

Each particle has position x,y,z, velocity vx,vy,vz,

size (might be sx,sy,sz, or one for each axis, so we will have ball-like particle),

mass, visual properties like color etc.

 

For chemistry reaction simulation there will be also needed formula to display on screen Na+, Cl-, H+, OH- etc.

and charge of ion-particle, electronegativity (?), etc. etc.

 

Each time step, for every particle in array, x is increased by vx, y+=vy,z+=vz

And collision detection is done between each particle with each other, and walls of container where they reside.

Checking each 1 mln vs 1 mln other particles in brute-force way (equation of intersection of sphere vs sphere, you probably know?) is 10^12 operations.

It's very time consuming process, therefor there is need for kd-tree, octree etc. algorithms to speed it up.

If there is found collision, in particle physics simulations, like in attached videos above, there is just done recalculation of velocity vectors (with some randomization, so each time they go in slightly different direction, while maintaining momentum/energy).

In chemistry version of simulator there would be also needed to check whether there is reaction between one particle-molecule and other particle-molecule.

There is also need to take care of charged particles, repelling same, attracting opposite (influencing vx,vy,vz of each particle).

 

Additionally make visualization of this in OpenGL so user can see and rotate views in the middle of process.

 

If Komnen wouldn't be able to do it brute-force way, like I described above,

he would fail miserably with much more advanced version suggested by hypervalent_iodine..

 

Komnen,

maybe you should start from making C/C++ command-line tool which is taking list of chemical formulas as argv[] arguments,

and showing user whether it's balanced equation to stdio,

and eventually show properly balanced equation.. ?

It would be good start for beginner in chemistry.

 

You should ask your friends what they think about above ideas.

Edited by Sensei

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Sensei, do u have any idea is it necessary to have sophisticated apparatus to realize your idea that proposed above ?

 

It is obvious we need computers but I ask

more in chemical aspect

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Sensei, my main point was that I wasn't sure if what you suggested would be of any interest to current research. It seems a bit simple to me, though it touches on more interesting kinetic modelling.

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At what level?

 

Generally, I would say that there is almost no mathematics in chemistry apart from basic numeracy. There are exceptions like quantum chemistry, molecular dynamics and similar. And even then, the level of mathematics will depend on personal preferences to a large extent.

 

 

Chemistry is far from my interests -...

It shows.

The idea that " there is almost no mathematics in chemistry apart from basic numeracy." is absurd.

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It shows.

The idea that " there is almost no mathematics in chemistry apart from basic numeracy." is absurd.

 

Can you expand on that with some nice examples that really are beyond arithmetic, basic calculus, linear algebra and integral transforms?

 

One thing that has been touched upon is 'mathematical chemistry', which does use some graph theory, combinatorics and topology. There is also quantum chemistry, but I think as dealing with more than a few interacting particles explicitly is impossible one resorts to numerical methods - I am not sure that many people in this field really need deep results from topological algebra, operator theory and spaces.

 

Chemical engineering - as suggested in this thread - uses numerical modelling of various phenomena.

 

There will also be the need for some basic statistics and data analysis - it depends on who you ask if this is really mathematics.

 

I know that some group theory can also be useful, but I doubt many chemists are well-versed in groups. For sure group theory is needed in spectroscopy - but how much beyond basic group theory does one need here?

 

I would be very happy to be corrected and shown how advanced mathematics is part of a typical chemists tool kit.

Edited by ajb

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So true John!

Can you point to some results to back up what you are supporting?

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Can someone give me any ide for any study which includes Mathematic and Chemistry in one study?

 

I have to say that both ajb and I and perhaps also others took this to mean that you wanted to study mathematical chemistry in a formal course.

 

Do you really mean that you simply want to apply your maths to help your flatmates in some way, as a private project?

 

 

Hypervalent iodine is right to say that you need some knowledge of chemistry to do this effectively.

 

Note the word apply,

Chemists' use of mathematics is applied.

I can't imagine your flatmates being interested in the pure mathematics supporting the applications.

Further many of the applications spring from the border area between Chemistry and Physics

 

So much so that on of the leading textbooks of the last century was entitled

 

The Mathematics of Physics and Chemistry By Margenau and Murphy.

 

Most of the group theory developed there is for crystal chemistry.

 

Also look at the more modern

 

The Chemistry Maths Book : Steiner

 

I previously mentioned reaction kinetics.

Some of this is at the forefront of applied maths and includes (systems of) differential equations not all of which have known solutions and many of which are non linear in character.

 

The emphasis placed on the basic principles that underpin both Physics and Chemistry is different, no more so than in Quantum Mechanics.

Physicists tend to concentrate on primary particles - atoms and below.

Chemists are more interested in combinations of atoms, called molecules.

So a look at high level quantum chemistry takes on quite a different view from high level quantum physics, although the same underlying science is still there.

 

Contemporary Quantum Chemistry : Goodisman

 

Molecular Quantum Mechanics : Atkins and Friedman

 

QM is also bound up with another mathematical area common to maths and physics, spectroscopy.

 

Spectroscopy : Whiffen.

 

Apart from the above books, another area of rapid modern development is the mathematics of electrochemistry

 

Modern Electrochemistry : Bockris and Reddy

Edited by studiot

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Ajb, with respect, you can't both claim that chemistry is outside your area of interest and then make assumptions about what a typical chemist does or does not know.

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Ajb, with respect, you can't both claim that chemistry is outside your area of interest and then make assumptions about what a typical chemist does or does not know.

 

 

Okay, so correct me!

 

Looking at the syllabus of a few universities it does not seem that a typical student leaving with an undergrad education will have been exposed to any high brow mathematics - the same is true of typical physics educations.

 

After that things will depend a lot more on the tastes and interests of the individuals - chemistry research covers a lot of things including things boarding with theoretical physics.

Edited by ajb

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