Book:Lecture Notes
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Lecture Notes
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Algebra
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
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
Geometry
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
Analysis
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
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
Combinatorics
- 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
Calculus
- 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
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