Complete undergraduate bundle-pack [closed]

Using some of the recommendations Others gave me and the Stanford math major checklist I have made the following list: One should read all books corresponding to a subject (in order) not just one of them.. The first part is a requirement while in the second part students usually take at least 2 electives ( I give 4 examples).

Calculus:

Calculus by Michael Spivak

Calculus volumes 1 and 2 by Tom M.Apostol

Analysis

Principles of Mathematical Analysis by Walter Rudin

Real and complex analysis by Walter Rudin

Topology

Topology by James Munkres or

General Topology by Stephen Willard (harder)

Linear Algebra

Linear Algebra by Friedberg,Insel and Spence

Differential Equations:

Ordinary Differential Equations by Tenenbaum and Polland

Partial Differential equations by Lawrence C evans.

Algebra

Abstract Algebra by Dummit and Foote

Combinatorics

Introductory Combinatorics by Brualdi

Set theory:

Introduction to set theory by Hrbacek and Jech

Electives:

Algebraic Topology

Algebraic Topology: an introduction by W.S Massey

Algebraic Geometry

Undergraduate algebraic geometry by Miles Reid

Number theory:

An introduction to the theory of numbers by Hardy and Wright

Algebraic number Theory (If you also take Number theory)

Algebraic Theory of numbers by Pierre Samuel.


Here's one possible list.

Principles of Mathematical Analysis by Walter Rudin

Topology by James Munkres

Linear Algebra by Friedberg, Insel, and Spence

Abstract Algebra by Dummit and Foote


This is a blog which describes on how to be a pure mathematician. You can go through it and find out what all opportunities you have in various fields of mathematics.


Here is another useful list.

This is a link to the Mathematics Programs offered at the University of Toronto (St. George):

http://www.artsandscience.utoronto.ca/ofr/archived/1213calendar/crs_mat.htm

A course number with a Y indicates a full year course (72 hrs of lecture) and a course number with H indicates a half year course (36 hrs of lecture):

First Year

MAT157Y1 - Analysis I Text: Calculus by Spivak. Used in the past: Principles of Mathematical Analysis by Rudin.

If you have never been exposed to abstract mathematics Spivak is probably better to go with. UofT has been teaching from Spivak's for awhile now.

MAT240H1 & Mat247H1: Linear Algebra I & II Text: Linear Algebra by Friedberg et al. Used in the past: Linear Algebra Done Right by Axler.

Second Year

MAT257Y1 - Analysis II

Text - Analysis on Manifolds by Munkres Used in th past: Calculus on Manifolds by Spivak

Go with Munkres on this one. Spivak is barely a little over 100 pages in length! So you can imagine how terse it is.

MAT267H1 - Advanced Ordinary Differential Equations Text - Differential Equations, Dynamical Systems, & Introduction to Chaos by Hirsch et al. & Elementary Differential Equations by Boyce and DiPrima

Third Year

MAT347Y1 - Groups, Rings, & Fields Text: Abstract Algebra by Dummit and Foote

MAT354H1 - Complex Analysis I Text: Complex Analysis by Stein & Shakarchi. Used in the past: Real and Complex Analysis by Rudin

MAT315H1 - Introduction to Number Theory Text: An Introduction to the Theory of Numbers by Niven. Used in the past: A Friendly Introduction to Number Theory by Silverman.

MAT344H1 - Introduction to Combinatorics Text: Applied Combinatorics by Tucker

MAT327H1 - Introduction to Topology Text: Topology by Munkres.

MAT357H1 - Real Analysis I Text: Real Mathematical Analysis by Pugh. Used in the past: Real and Complex Analysis by Rudin.

MAT363H1 - Introduction to Differential Geometry Text: Elementary Differential Geometry by Pressley.

Fourth Year

A lot of these courses are cross listed so they're actually graduate courses. Check here for texts and references:

http://www.math.toronto.edu/cms/tentative-2012-2013-graduate-courses-descriptions/

Hope this helps!