Question about what math to take.

1. Sep 26, 2010

Ostonzi

For biotech/biochem/biology? Or something just really interesting to take.

Next year I can take 2 of these.

Fourier Analysis
Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform

Mathematical Logic
Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic.

Intro to Topology
Set theory. Euclidean/metric spaces. Basics of general topology, including compactness/connectedness.
.

Mathematical Analysis of Biological Networks
Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks

Sequences, Series, and Foundations
Introduction to mathematical reasoning used in advanced mathematics. Elements of logic. Mathematical induction. Real number system. General, monotone, recursively defined sequences. Convergence of infinite series/sequences. Taylor's series. Power series with applications to differential equations. Newton's method.

Complex Analysis
Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues.

Elementary PDEs I/II
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks.

Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems.

Introduction to Ordinary Differential Equations
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors.

Linear Programming and Combinatorial Optimization
Simplex method, connections to geometry, duality theory,sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportationproblems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems.

Enumerative Combinatorics
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics.

Dynamical Systems and Chaos
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets.

I was thinking of doing topology for fun.

Last edited: Sep 26, 2010
2. Sep 26, 2010

ODE's and Intro to Bio networks sound like interesting classes that could be relevant to biology.

3. Sep 26, 2010

chingkui

If you are looking for something immediately useful for biotech or any science, the obvious choice would be ODE/PDE/Linear algebra. If you are looking for fun, then it depends on what your interest is, and whether you are well-prepared to take the classes of your choice.

4. Sep 26, 2010

Ostonzi

Well the prereqs for these classes are only linear algebra/differential equations and multivariable calculus which would be fulfilled. Some of these require sequences, series, and foundations though.

I crossed off ones that I don't feel all that interested in.

5. Sep 26, 2010

l'Hôpital

The U Of M, huh?

How much do you like proofs? Or perhaps a better question is, can you do proofs? Are you scared by them?

From my understanding, Complex Analysis and Fourier Analysis are fantastic for Engineers and Physicists. Sequences and Series is/was a waste of time for me when I took it, but I hear that it's constantly getting better. Thus, definitely professor-oriented. If Mosher is teaching it, take it.

I took ODEs but I can't comment, since my year was (or so I was told) different from others. Less Dynamical Systems, more other stuff.

6. Sep 26, 2010

lisab

Staff Emeritus
I thought those were the two that were most relevant, too.

7. Sep 27, 2010

Ostonzi

What about dynamical systems?