Book:Lecture Notes

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Lecture Notes

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Abstract Algebra
R.B. Ash: Abstract Algebra
Paul Garrett: Abstract Algebra
Paul Garrett: Intro to Abstract Algebra (Solutions)
D. Surowski: A Workbook in Higher Algebra
Linear Algebra
H. Connell: Elements of Abstract and Linear Algebra
J. Hefferon: Linear Algebra
A. Baker: Basic Linear Algebra
W.W.L. Chen: Linear Algebra
Group Theory
J.S. Milne: Group Theory
P. Cvitanović: Group Theory: Birdtracks, Lie's and Exceptional Groups
Paul Garrett: Buildings, BN-Pairs, Hecke Algebras, Classical Groups
R.B. Howlett: Miscellaneous Facts About Coxeter Groups
Introduction to Group Theory
A. Baker: Groups and Symmetry
Representation Theory
A. Baker: Representations of Finite Groups
C. Teleman: Representation Theory
P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, and E. Yudovina: Introduction to representation theory
Universal Algebra
G.M. Bergman: An Introduction to Universal Algebra
S. Burris and H.P. Sankappanavar: A Course in Universal Algebra
M. Valeritoe: Lectures on Universal Algebra
Lie Groups
B.C. Hall: An Elementary Introduction to Groups and Representations
Paul Garrett: Lie Algebras and Lie Groups
I. Avramidi: Notes on Lie Groups
R.L. Bryant: An Introduction to Lie Groups and Symplectic Geometry
A. Cap: Lie Groups
Galois Theory
J.S. Milne: Fields and Galois Theory
D. Wilkins: Galois Theory
A. Baker: An Introduction to Galois Theory
J.P. Serre: Topics in Galois Theory
M. Reid: Galois Theory
S.R. Ghorpade: Notes on Galois Theory
Lattice Theory
Stanford handout on Lattice theory
Commutative Algebra
R.B. Ash: Commutative Algebra
Paul Garrett: Homological and Commutative Algebra
D. Murfet: Matsumura: Commutative Algebra
S.R. Ghorpade: Lectures on Commutative Algebra
Category Theory
M. Fokkinga: A Gentle Introduction to Category Theory
M. Bar and C. Wells: Toposes, Triples and Theories
J. van Oosten: Basic Category Theory
D. Turi: Category Theory Lecture Notes
D.E. Rydeheard and R.M. Burstall: Computational Category Theory

Number Theory

W.W.L. Chen: Elementary Number Theory
W.W.L. Chen: Distribution of Prime Numbers
J.S. Milne: Algebraic Number Theory
R.B. Ash: Algebraic Number Theory
J.S. Milne: Modular Functions and Modular Forms
Paul Garrett: Modular Forms and L-Functions
I.V. Dolgachev: Modular Forms
J.S. Milne: Etale Cohomology
J.S. Milne: Class Field Theory
J.S. Milne: Complex Multiplication
J.S. Milne: Abelian Varieties
Paul Garrett: Number Theory
Paul Garrett: Cryptography and Number Theory
Paul Garrett: Coding Theory
A. Baker: An Introduction to $p$-adic Numbers and $p$-adic Analysis
A. Baker: Algebra and Number Theory
I. Connell: An Elliptic Curve Handbook


Algebraic Geometry
J.S. Milne: Algebraic Geometry
J.S. Milne: Algebraic Groups
I.V. Dolgachev: Introduction to Algebraic Geometry
I.V. Dolgachev: The McKay Correspondence
I.V. Dolgachev: Topics in Classical Algebraic Geometry
C. Weibel: An Introduction to Algebraic K-Theory
Differential Geometry
B. Csikós: Differential Geometry
G. Lugo: Differential Geometry
M. Kazarian: Differential Geometry
T. Shifrin: Differential Geometry: A First Course in Curves and Surfaces
D. Zaitsev: Differential Geometry: Lecture Notes
J.-P. Demailly: Complex Analytic and Differential Geometry


Complex Analysis
R.B. Ash: Complex Variables
Paul Garrett: Complex Analysis
G. Cain: Complex Analysis
H.V. McIntosh: Complex Analysis
W.W.L. Chen: Introduction to Complex Analysis
Real Analysis
R.B. Ash: Real Variables with Basic Metric Space Topology
S. Semmes: Elements of Linear and Real Analysis
J. Orr: Analysis WebNotes
I. Craw: Advanced Calculus and Analysis
W.W.L. Chen: Fundamentals of Analysis
Functional Analysis
W.W.L. Chen: Linear Functional Analysis
W.W.L. Chen: Introduction to Lebesgue Integration
T. Ward: Functional Analysis
Paul Garrett: Functional Analysis

Differential Equations

E.M. Harrell and J.V. Herod: Linear Methods of Applied Mathematics

Probability and Statistics

R.B. Ash: Lectures on Statistics
R.B. Ash: Basic Probability Theory
C. Grinstead and J. Snell: Introduction to Probability
N. Vaillant: Probability Tutorials

Complexity and Algorithms

C. Yap: Fundamental Problems in Algorithmic Algebra
C. Yap: Introduction to Complexity Classes
C. Yap: Robust Geometric Computation
C. Yap: Algorithmics
W.W.L. Chen: Discrete Mathematics


M. Petkovsek, H. Wilf and D. Zeilberger: The Book A=B
H. Wilf: Generatingfunctionology
D. Feldman: Ramsey's Theorem and Ramsey Theory
Dynamic Surveys in Combinatorics

Basic Algebra

K. Kubota: College Algebra
D. Joyce: A Short Course in Trigonometry
T. Ward: Basic Mathematics
W.W.L. Chen: Miscellaneous Topics in First Year Mathematics
MathIsFun: College Algebra


G. Cain and J. Herod: Multivariable Calculus
Harvey Mudd College Calculus Tutorials
D. Sloughter: Difference Equations to Differential Equations
P. Dawkins: Paul's Online Math Notes
W.W.L. Chen and X.T. Duong: Elementary Mathematics
W.W.L. Chen: First Year Calculus
W.W.L. Chen: Multivariable and Vector Analysis

Graph Theory

R. Diestel: Graph Theory

Dynamical Systems

G. Elert: The Chaos Hypertextbook
P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, G. Vattay, N. Whelan and A. Wirzba: Chaos: Classical and Quantum
J. Milnor: Dynamics in One Complex Variable
P. Arnoux, V. Berthé, S. Ferenczi, S. Ito, C. Mauduit, M. Mori, J. Peyrière, A. Siegel, J.-I. Tamura and Z.-Y. Wen: Substitutions in Dynamics, Arithmetic and Combinatorics
T. Ward: Entropy of Compact Group Automorphisms
T. Ward: Valuations and Dynamics


C. Johnson and M. Burnett: Crystallographic Topology
S.A. Morris: Topology Without Tears
Algebraic Topology
A. Hatcher: Vector Bundles and K-Theory
T. Ward: Algebraic Topology


S. Bilaniuk: A Problem Course in Mathematical Logic

MIT Online Materials