Drexel University

Mathematics Student Organization

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Notes and Online Books on Various Subjects:

Here is a few sets of notes we found on various topics that you may have some interest in.

Real Analysis

Real Analysis With Basic Metric Space Topology--Ash

Theory of Functions of a Real Variable--Sternberg

Limits and Continuity, Open and Closed Sets, and Metric Spaces (Wilkins Analysis and Topology Course Pt. I)--Wilkins

Topological Spaces (Wilkins Analysis and Topology Course Pt. II)--Wilkins

Normed Vector Spaces and Functional Analysis (Wilkins Analysis and Topology Course Pt. III)--Wilkins

Topology in the Plane (Wilkins Analysis and Topology Course Pt. IV)--Wilkins

A Course in Analysis--Wilkins

Real Analysis Lecture Notes--Kish

 

Miscellaneous Analysis

Fourier Analysis (Pt. I)--Thiele

Fourier Analysis (Pt. II)--Thiele

Functional Analysis--Serfaty

 

Topology

The Geometry and Topology of 3-Manifolds-- Thurston

Algebraic Topology--Wilkins

Topological and Metric Spaces--Korner

General Topology--Moller

Lecture Notes on Algebraic Topology--Wu

General Topology--Schapira

Introduction to General Topology--Hoffman

 

Algebra

Elements of Abstract and Linear Algebra-- Connell

A Course in Universal Algebra-- Sankappanavar and Burris

Abstract Algebra: The Basic Graduate Year-- Ash

A Course in Commutative Algebra--Ash

Lie Algebras--Sternberger

Toposes, Triples, and Theories-- Barr and Wells

Introduction to Vectors and Tensors: Linear and Multilinear Algebra (Vol. I)--Bowen and Wang

Introduction to Vectors and Tensors: Linear and Multilinear Algebra (Vol. II)--Bowen and Wang

Abelian Categories--Freyd

Categories and Groupoids-- Higgins

Basic Concepts of Enriched Category Theory--Kelly

Abstract and Concrete Categories: The Joy of Cats--Adamek, Herrlich, and Strecker

Representations of Finite Groups--Baker

An Introduction to Galois Theory-- Baker

Groups and Symmetry-- Baker

Basic Linear Algebra-- Baker

Topics in Commutative Algebra--Wilkins

Galois Theory--Wilkins

Abstract Algebra--Wilkins

Abstract Algebra Done Concretely--Arapura

Field Theory--Clark

Intro to Abstract Algebra--Garrett

Lecture Notes, Based on Hungerford Algebra, Abstract Algebra--Meierfrankenfeld

Fields and Galois Theory--Milne

Lecture Notes on Semigroups--Harju

Representation Theory--Serganova

Lecture Notes and Problems in Representation Theory--Etingof

Group Theory--Milne

Class Field Theory--Milne

Algebraic Groups and Arithmetic Groups--Milne

Complex Multiplication--Milne

A Primer of Commutative Algebra--Milne

 

Complex Analysis

Complex Variables--Ash

Complex Analysis-- Thiele

Basic Theorems in Complex Analysis (Wilkins Course in Complex Analysis Pt. I)--Wilkins

Infinite Series (Wilkins Course in Complex Analysis Pt. II)--Wilkins

Winding Numbers of Closed Paths in the Complex Plane (Wilkins Course in Complex Analysis Pt. III)--Wilkins

Path Integrals in the Complex Plane (Wilkins Course in Complex Analysis Pt. IV)--Wilkins

Holomorphic Functions (Wilkins Course in Complex Analysis Pt. V)--Wilkins

Cauchy's Theorem (Wilkins Course in Complex Analysis Pt. VI)--Wilkins

Basic Properties of Holmorphic Functions (Wilkins Course in Complex Analysis Pt. VII)--Wilkins

Applications of Cauchy's Residue Theorem (Wilkins Course in Complex Analysis Pt. VIII)--Wilkins

Elliptic Functions (Wilkins Course in Complex Analysis Pt. IX)--Wilkins

Complex Analysis Lecture Notes--Rybkin and Fairbanks

 

Probability Theory

Introduction to Probability and Random Processes-- Baclawski and Rota

Basic Probability Theory-- Ash

 

Combinatorics

Generating functionology-- Wilf

Algebraic Combinatorics--Helleloid

Combinatorial Enumeration--Harju

 

Number Theory

A Course in Algebraic Number Theory-- Ash

Elementary Number Theory: Primes, Congruences, and Secrets--Stein

Algebra and Number Theory--Baker

An Introduction to p-adic Numbers and p-adic Analysis--Baker

Number Theory-Lecture Notes--Ionascu

Algebraic Number Theory-- Milne

Algebraic Number Theory--Clark

Modular Functions and Modular Forms--Milne

 

Graph Theory

Graph Theory--Diestel

Graph Theory with Applications--Bondy and Murty

Graph Theory--Wilkins

Lecture Notes on Graph Theory--Harju

 

Geometry

Differential Geometry (Pt. I)--Wilkins

Differential Geometry (Pt. II)--Wilkins

Differential Geometry (Pt. III)--Wilkins

Problem Set for Differential Geometry by Wilkins-- Wilkins

Solution to Problem Set for Differential Geometry by Wilkins-- Wilkins

Introduction to Differential Forms--Arapura

Tensor Calculus--Grinfeld

 

Algebraic Geometry

Algebraic Geometry Over the Complex Numbers--Arapura

Algebraic Geometry--Milne

Abelian Varieties--Milne

Lectures on Etale Cohomology--Milne

 

Set Theory

Lectures Notes on Ordered Sets--Harju

 

Miscellaneous

Many More Notes by Pete L. Clark