Recommended College Math Courses

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SUMMARY

Math majors should consider taking advanced courses beyond the basic requirements, including Algebraic Topology, Differential Geometry, and Complex Analysis. Essential topics also include Numerical Analysis, Stochastic Variables, and Functional Analysis. Courses in Cryptography, Graph Theory, and Combinatorics are recommended for applied mathematics enthusiasts. A solid foundation in Differential Equations is crucial, as it supports various advanced mathematical concepts.

PREREQUISITES
  • Advanced Algebra and Analysis
  • Understanding of Topology and Differential Geometry
  • Knowledge of Differential Equations
  • Familiarity with Stochastic Variables and Probability
NEXT STEPS
  • Research Algebraic Topology and its applications
  • Explore Differential Geometry and its relevance in various fields
  • Learn about Numerical Analysis techniques and tools
  • Investigate the principles of Cryptography and its mathematical foundations
USEFUL FOR

Math majors, applied mathematicians, and anyone interested in deepening their understanding of advanced mathematical concepts and their applications in various fields.

vivalavida
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which courses would you recommend a math major to take beyond the major requirements? I feel like 2 semesters in algebra, analysis, and topology are the basic necessities. Should I look at anything else? Any suggestions in applied maths?
 
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Differential Geometry was a fun extracurricular course, also Cryptography.
 
elliptic integrals-learn about those
extremely useful
 
Numerical analysis? Graph theory and combinatorics? Theoretical CS? Algorithms? Classical / Quantum / Relativistic / Statistical / Fluid / Solid mechanics? Economics?
 
The essential thing missing from your list is a year of algebraic topology / differential geometry.
 
I would take courses on stochastic variables and calclulus.
 
You will probably need complex analysis. Functional analysis and differentiable manifolds are also very useful.
 
elfboy said:
elliptic integrals-learn about those
extremely useful

How are these useful?
 
are differential equations included in the basic courses?
 
  • #10
There tons of useful math, it depends on what are you specializing... and sometimes it depends on your research...
 
  • #11
Combinatorics and probability were fun.
 
  • #12
Once someone gets algebra and analysis (the real stuff, not an introductory course) down, I suppose next are some topology (algebraic too!) ODE, and differential geometry. But if someone comes this far, the person surely knows what to do?
 

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