Math course guidance

[Link]

Main Question or Discussion Point

I'm in the math Higher level course in the International Baccalaureate programme, and it offers a choice of one from four topics during the final year to study in depht. Now i have a hard time chosing one, so I would appreciate if someone could gimme some tips

The subjects are: Statistics and probability, Sets groups and relations, Series and differential equations and discrete mathematics.

Now my interests are in the field of physics and engineering, which leaves me with the choice of the later three. However i cant make a sound judgement since i have no idea what sets groups and relations are all about. Can someone gimme a brief of their respective applications/usefulness in university studies? Thanks.

 

[AKG]

You must be given some course descriptions. If you're interested in physics and engineering, then you probably don't need a course in statistics and probability (you will use some statistics and probability, but I don't think you need a course in it, you'll probably just use basic stuff they'll cover in science and engineering courses themselves). I can't imagine an engineer ever needing to know anything about set theory, not even a physicist actually. The course on sets, groups, and relations, is more of an abstract course focusing on more theoretical mathematics, and perhaps the basic ideas of sets that you need if pursuing theoretical mathematics. Again, I don't think you need this.

I asked if you had course descriptions because I'd like to know what exactly you'll do in "discrete mathematics." However, series and especially differential equations will be very useful for a physicist or an engineer, so I highly recommend that.

 

[mathwonk]

there is a subject called statistical mechanics which sounds as if it uses stat. group theory is about symmetry, a basic phenomenon in physics. indeed some of the theoretical physicists I have met studied mainly group representations.

nowadays physicists study also much more advanced ,math like vector bundles on complex curves.

of course everyone should know about series and DE. you sound as if you are just begining study of math. you should take as much as possible, but it is hard to see how you could go wrong with the series and de, if you have not had that yet.

 

[MalleusScientiarum]

I second mathwonk's suggestion. You cannot progress at all in physics without those two bodies of information.

 

[Brad Barker]

i'd have to agree, as well.

differential equations and series are indispensable for both physics and engineering.

those other topics you might pick up later on if your interests sway that way. (eg, if you become interested in theoretical physics, you might take a class that has group theory, or if you like computer science you might take a discrete math class.)

but diff eq is pretty fundamental to them both.



anyway, IMO, etc, etc.

 

[Link]

ok thanks to you all!

What i get out from it its like:

Statistics: Economists
Group, sets: Mathematicians
Series & diff equations: Engineers and physics
Discrete math: Computer people





Just one final request: Can you sort them according to the difficulty? I dont know many details, but what I do know from the course content:

Statistics: On to chi squared distribution
Set, groups: On to abelian, cyclic groups, Lagrange theorem
Series/diff. equations: Taylor, Maclaurain, L'Hopital
Discrete: Chinese remainder theorem, Fermats little theorem, hamiltonian cycles?

It might be just the beginning of maths, but its the hardest course our school got to offer, and im the only one in the school taking this course

 

[AKG]

It's really hard to tell by the content of the course (especially as briefly as you've given it) how difficult it will be. It depends on how the course is taught, of course, and also what you're good at.

 

[mathwonk]

the series and d.e. course looks much the hardest.

 

[ronggangsky]

I second Brad Barker's suggestion.
i major in physics! i think math is useful to all the students,

my english is poor,i cannt express myself freely,but i want to help you!

i want to make friends to you all,

 

[Brad Barker]

the series and d.e. course looks much the hardest.

really? i never thought that that stuff was very hard. :/

(maybe i should stop fearing my abstract algebra course, then! )



yeah, guessing the difficulty would be very difficult because it depends on your interests and abilities, the level of detail of the course content, the rapidity of teaching (self-instruction?), so on, so forth.

 

[Link]

Alright here is the full content (man, this sounds more like university stuff than high school stuff ) All courses are 40hrs and i got a teacher full time (the principal is nice to me )

Sets relations and groups:

Finite and infinite sets, subsets, operation on sets, subsets, intersection, complemet, set difference, symmetric difference
De Morgans laws
Ordered pairs
Relations, eqivalence relations and classes
Functions, injections, surjections, bijections. Composition of functions and inverse func.
Binary operations, associative distributive, commmuniative properties. Cayley tables.
Indentity element e
The inverse of an element a
Proofs of uniqueness of the identity and inverse elements
Axioms of group (G,*)
Abelian groups
The groups: R,Q,Z,C under addition, matrices of the same order under addition, 2x2 ivertible matrices under mupltiplication, integers under addition modulo n
groups of transformations
symmetries of an equilateral triangle, rectangle and square
invertible functions under composition of functions
permutations under composition of permutations.
Finite and infinite groups. Cyclic groups. Proof that all cyclic groups are abelian. Subgroups, proper subgroups. Lagranges theorem. Corollary to lagranges theorem. Isomorphism of groups.


Discrete maths:

Division and euclidian alrogrithms
ged(a,b), lcm(a,b)
Prime numbers and fundamental theorem of arithmetic
Representation of numbers in different bases (Heck I know this )
Linear diophantine equations
Modular arithmetic. Linear congruences. Chinese remainder theorem.
Fermats little theorem.
Graphs, verticles, edges, adjacent verticles, adjacent edges. Simple, connected, complete, planar, bipartile, trees, weighted graphs. Subgraphs. Graph isomorphism.
Walks, trails, paths, cycles, circuits. Hamiltonian paths and cycles, Euclidian trails and circuits.
Adjacency matrix. Cost adjacency matrix.
Graph algorithms, prims, Kruskals, Dijkstras.
Chinese postman problem
Travelling salesman problem. Upper/lower bounds algorithm.


Series and differential equations:

Infinite sequence of real numbers.
Limit theorems as n approaches infinity.
Limit of a sequence.
Improper integrals of the type (a)integral sign (infinity) f(x) dx
Integral as a limit of a sum, lower sum and upper sum
Convergence of infinite series
Partial fractions and telescoping series
Test for convergence
The p series sum(1/n^p)
Use of integrals to estimate sums of series
Series that converge absolutley, conditionally
Alternating series
Power series, ratio test
Taylor series, error term
Maclaurain series for e^x, sin x, cos x, arctan x, ln(1+x), (1+x)^p. Use of substitution to obtain other series.
Evaluation of limits in the form lim(x->a) f(x)/g(x) using l'hopital and taylor series.


Phew. Quite a lot of stuff to do for a high school diploma if i might comment upon my situation But sure its fun

 

[MalleusScientiarum]

There does not look to be much in the way of differential equations in your differential equations class.

From a physics standpoint, you will need pretty much all of the content at some point in all of the courses. Group theory is integral to the formulation of most modern theories, discrete math appears when dealing with computational physics, and the rest is just good general knowledge to have.

I still suggest the series and differential equations course, because in my opinion it's the easiest stuff out there. My second choice would be the group theory course.

 

[Link]

For you university students out there, do you read in all those stuff sooner or later in uni?

 

[rocketboy]

I'm in higher level IB math too! nice to see i'm not the only one :tongue2:

 

[James Jackson]

For advice as to what to take when, get the Calc stuff nice and sorted in your head. Stats is pretty important too, but the stats is easier to learn that the calc when it comes to statistical physics. Doing it the other way round is a bit silly really.

Group theory you won't touch until some advanced undergrad courses (such as field theory in QM), stats is useful, but not hard, whereas calc is there throughout. Similar for engineering I think.

 

[Brad Barker]

For you university students out there, do you read in all those stuff sooner or later in uni?

if i were in your shoes, i'd still go with taking the series option. (no diff eq in that course description! :surprised )


as far as the sets/groups stuff, i'm not even sure if i'd encounter that stuff as an undergrad if i weren't also a math major.

and i don't plan on taking a dedicated course in discrete math at all!

 

[leright]

What exactly is your major? If you're studying physics OR engineering then series/diffEQ AND prob/stats will be required courses, in addition to a complex analysis course and applied DE and linear alg.

 

[Brad Barker]

What exactly is your major? If you're studying physics OR engineering then series/diffEQ AND prob/stats will be required courses, in addition to a complex analysis course and applied DE and linear alg.

not necessarily.

at UF only ONE of those courses you listed are required for EITHER physics or engineering! (diff eq, and of course calcs I-III.)


(although i'll prob take every one of those courses anyway :tongue2: )

 

[leright]

not necessarily.

at UF only ONE of those courses you listed are required for EITHER physics or engineering! (diff eq, and of course calcs I-III.)


(although i'll prob take every one of those courses anyway :tongue2: )

for my EE degree, I need to take calc 1-3, diffEQ, advanced engineering math (complex analysis, applied DE, etc), and prob/stats.

Surprisingly, linear alg isn't a requirement for EE at my uni.

 

[Link]

alright i think i'll take series/diff. equation option. I dont know anything about the major system in university, but I want to be study aeronautical engineering or astrophysics, and I am only allowed to take ONE of the math option courses as there already is a 200 hour course before the option.
(thats all the high school math I will ever have )

 

[omagdon7]

That series curriculum is EXACTLY what was taught in my calc 2 class with the caveat that it leaves out volumes of rotation and polar coordinates.

 

[Stephan Hoyer]

You probably want to do the series option. That should give you almost exactly the same knowledge that you would get from the AP BC Calc and will probably work out more conviniently for going into university math courses. If I had taken a different option than the sequences and series option when I did IB HL math I would have been placed into a lower math class since that calculus stuff is all required for more advanced courses such as linear algebra and vector calculus. It may not perhaps seem like the most interesting option (I had no choice in my class of 15) but it is probably the most useful.

 

[Link]

Ok thank you all! I am the only student in the class so that is why I started the thread inthe first place