Undergraduate mathematics for an engineer

[medwatt]

I am an electrical engineer who is fascinated by mathematics. As you might expect, electrical engineering uses a lot of advanced concepts in mathematics from differential equations, linear algebra, calculus, complex analysis etc. However I would like to continue reading maths on my own.
I would like anybody who has finished undergraduate maths list down the subjects in the order they were studied at the university because order matters when studying maths.
eg.
First year.
1. College algebra
2. Introduction to Linear Algebra
3. Calculus 1
4. Statistics
etc etc etc

Please take my request seriously because I am serious about furthering my mathematical knowledge individually.
Thanks.

 

[HallsofIvy]

I am going to assume that "college algebra" does NOT refer to "abstract algebra". In that case a reasonable order would be
College Algebra
Calculus I and then higher levels of Calculus
Statistics
Introduction to Linear Algebra
Ordinary Differential Equations
Partial Differential Equations

 

[medwatt]

what about topics like Group Theory, Topology . . . things that are not done in engineering courses . . . where will their location be . . . all of the topics listed above I did in university with just introduction to PDE rather than anything indepth (Laplace equation, wave equation)

 

[Klungo]

Math branches out. That is, you could go from analysis 1 to analysis 168 without ever taking abstract algebra, topology, etc. The only importance of order is from analysis 1 to analysis 2 to ... analysis 168.

Look at texts, syllabii, descriptions set out for courses at your university.

I too am an EE major with a a chuck of my undergraduate coursework set for pure mathematics. (Since I have 0 gen eds left and am taking upper division linear algebra on arrival). I was more worried not with order but what subjects as a whole would give me the most diverse experience of undergraduate mathematics across all availble fields.

Edit: I am assuming you're an EE major.

 

[medwatt]

No. I just finished EE a year ago but I had always wanted to become a mathematician !

 

[Klungo]

Ah. Well, I would still recommend looking at syllabii/course descriptions of courses from your former university(ies) that you believe you meet the prerequisites for and that interest you. Find the course text, go to google books and match course topics to the appropriate chapters that appear on the table of contents and you will have you order.

Note: Usually, a single text can span more than one course of that field and has maintains its personality from cover to cover.

Many texts appear in "who wants to be a mathematician" sticky in the top of the forum by mathwonk.

 

[Studiot]

Maths has become an enormous field. Too big for anyone person.

Some books that might take you on beyond what you already know and introduce serious areas of mathematics that might be of interest.

Differential Geometry : Prakash

Elementary Differential Geometry : O'Neill

Applied Functional Analysis : Griffel

Introductory Functional Analysis with Applications : Kreysig

Discrete Mathematics : Biggs

Discrete Mathematics for New Technology : Garnier and Taylor

Introduction to Topological and Metric Spaces : Sutherland

Introduction to Group Theory : Ledermann