- #1

PeteyCoco

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I just got a math minor appended to my physics major. I'm registering for courses next week, but I'm having a bit of difficulty choosing math courses. None of them have prerequisites, but the prof I met with today did say that some would be very difficult without having developed mathematical maturity. The courses I am choosing between are:

Mathematical rigour: proofs and counter-examples; quantifiers; number systems; Cardinality, decimal representation, density of the rationals, least upper bound. Sequences and series; review of functions, limits and continuity

Introduction to the ring of integers and the integers modulo N. Groups: definitions and examples; sub‑groups, quotients and homomorphisms (including Lagrange’s theorem, Cayley’s theorem and the isomorphism theorems). Introduction to the Cauchy and Sylow theorems and applications

Now my mathematical maturity is pretty weak in terms of proofs, but I do well in my physics courses where vector cal is used (I'm finishing up Griffiths' Electrodynamics and can tackle most problems in it). Would these courses be too much for someone new to formal mathematics like me?

My other option is to take Linear Algebra I & II next year as a way to improve my mathematical abilities before moving up to these courses:

Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization.

I've covered most of the material mentioned in this blurb, but it was in a course for physicists and we used Elementary Linear Algebra by Anton. Should I just ease my way into math, starting with Linear Algebra I & II? There's no time pressure.

**Analysis I****Textbook: Introductory Real Analysis - Dangello & Seyfried**Mathematical rigour: proofs and counter-examples; quantifiers; number systems; Cardinality, decimal representation, density of the rationals, least upper bound. Sequences and series; review of functions, limits and continuity

**Abstract Algebra I****Textbook: Abstract Algebra - Dummit & Foote**Introduction to the ring of integers and the integers modulo N. Groups: definitions and examples; sub‑groups, quotients and homomorphisms (including Lagrange’s theorem, Cayley’s theorem and the isomorphism theorems). Introduction to the Cauchy and Sylow theorems and applications

Now my mathematical maturity is pretty weak in terms of proofs, but I do well in my physics courses where vector cal is used (I'm finishing up Griffiths' Electrodynamics and can tackle most problems in it). Would these courses be too much for someone new to formal mathematics like me?

My other option is to take Linear Algebra I & II next year as a way to improve my mathematical abilities before moving up to these courses:

**Linear Algebra I****Textbook: Linear Algebra - Friedberg, Insel, & Spence**Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization.

I've covered most of the material mentioned in this blurb, but it was in a course for physicists and we used Elementary Linear Algebra by Anton. Should I just ease my way into math, starting with Linear Algebra I & II? There's no time pressure.

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