Which math courses for Math minor with CS major?

[Jarvis323]

I'm a CS major planning minoring in Math. The math minor requires 20 units ( 5 courses ) of upper division math but doesn't restrict you to choosing any specific set of courses. I guess I'm interested in courses which will compliment computer science and prepare me for grad school.

Introduction to Abstract Mathematics
Number Theory A,B
Differential Geometry
Convex Geometry
Partial Diff Eq. A,B,C
Ordinary Diff Equations A,B
Real Analysis A,B,C
Numerical Analysis A,B,C
Fourier Analysis
Mathematical Finance
Probability A,B
Euclidean Geometry
Combinatorics
Algebraic Combinatorics
Discrete Mathematics
Modern Algebra A,B,C
Mathematical Foundations of Database Theory, Design and Performance
Mathematics and Computers
Applied Linear Algebra
Optimization
Complex Analysis A,B

The main areas of CS I'm interested in are scientific computing, scientific visualization / computer graphics, and high performance systems / parallelism /distributed systems.

Any opinions on which math courses I should take?

 

[Poley]

Number theory, combinatorics, discrete mathematics, modern algebra, and linear algebra all have immediate applications in CS. Numerical analysis and PDEs are important in scientific computing.

Real analysis and complex analysis will probably be less useful in CS applications, but they are very standard topics, so if you want to acquire a broader background in math I would recommend those.

It's hard to know what "Introduction to Abstract Mathematics" and "Mathematics and Computers" are without course descriptions, but these might be good choices as well.

 

[Jarvis323]

Thank for the input Poley. I've decided to take Numerical Analysis 1, 2, 3, Partial Differential Equations 1, and Applied Linear Algebra.

I might also take a few courses like discrete math, probability and statistical modelling, for technical electives as part of the CS degree.

What is your opinion on taking P.D.E's {1}, {1, 2} or {1, 2, 3}, given the descriptions below; in terms of scientific computing.

Partial Differential Equations 1 :

    Derivation of partial differential equations; 
    separation of variables; 
    equilibrium solutions and Laplace's equation; 
    Fourier series; 
    method of characteristics for the one dimensional wave equation. 
    Solution of nonhomogeneous equations. 

Partial Differential Equations 2 :
  
    Sturm-Liouville Theory;  
    self-adjoint operators; 
    mixed boundary conditions; 
    partial differential equations in two and three dimensions; 
    Eigenvalue problems in circular domains; 
    nonhomogeneous problems and the method of eigenfunction expansions; 
    Poisson’s Equations

Partial Differential Equations 3 :

    Green’s functions for one-dimensional problems and Poisson’s equation; 
    Fourier transforms; Green’s 
    Functions for time dependent problems; 
    Laplace transform and solution of partial differential equations.

And do you think that Ordinary Differential Equations is worth considering?

Ordinary Differential Equations 1:

    Scalar and planar autonomous systems; 
    nonlinear systems and linearization; 
    existence and uniqueness of solutions; 
    matrix solution of linear systems; 
    phase plane analysis; stability analysis; bifurcation theory; 
    Liapunov's method; 
    limit cycles; 
    Poincare Bendixon theory.

Do you think I ought to take all three Numerical Analysis courses, and all of the P.D.E.'s, or should I save a a few slots to get a broader education in Mathematics?

 

[MathWarrior]

I am doing the same thing, except my minor is more thorough apparently; discrete mathematics is usually required for a CS major. It usually touches on logic, recursion, big-oh notation, introductory combinatorics, discrete probability, induction, introductory number theory, introductory graph theory, set theory, relations, and automata.

Combinatorics is extremely useful if you want to analyze algorithms, modern algebra and number theory are both super useful if you intend to do anything with cryptography. Abstract algebra (modern algebra) however can be applied to more things then just cryptography, such as error correcting codes (coding theory), switching circuits, etc.

Numerical analysis is good if you are mainly interested in scientific computing.

Optimization is also a good choice if you like scientific computing, simplex algorithm for example.

In my opinion, every computer scientist should be good at linear algebra especially if you have even the remote interest in graphics.

Having taken ordinary differential equations, I would recommend this mainly if you were intending to do scientific computing, or PDE's, some of the concepts from it are directly applied to your partial differential equations courses. Differential equations are also good for control theory, if you have an interest in that.

 

[Jarvis323]

discrete mathematics is usually required for a CS major. It usually touches on logic, recursion, big-oh notation, introductory combinatorics, discrete probability, induction, introductory number theory, introductory graph theory, set theory, relations, and automata.

Discrete math for CS is required, but the Discrete Mathematics course I listed is an upper division math course which covers different material.

Here's the description,

Coding theory, error correcting codes, finite fields and the algebraic concepts needed in their development.

 

[Hercuflea]

if your school offers two semesters of discrete math and two semesters of abstract algebra and two semesters of linear algebra, take all of those and that should be enough for a minor. All are heavily related to cs.