Probability and graphs

• Concentration-of-measure inequalities, Lugosi, Notes'03
• Markov Chains, Norris
• Reversible Markov Chains and Random Walks on Graphs, Aldous
• The Probabilistic Method, Alon, Spencer
• Random Graphs, Janson, Luczak, Rucinski
• Random Graphs, Bollobas

Geometry, spectra, matrices and embeddings

• Lectures on Discrete Geometry, Matousek
• The Random Projection Method, Vempala
• Convex Bodies, Bonnesen, Fenchel
• Matrix Analysis, Horn, Johnson
• Topics in Matrix Analysis, Horn, Johnson
• Matrix Computations, Golub, van Loan
• Introduction to Circle Packing, Stephenson
• The Discrepancy Method, Chazelle

Algorithms and optimization

• Approximation Algorithms for NP-Hard Problems, Hochbaum
• Combinatorial Optimization, Cook, Cunningham, Pulleyblank, Schrijver
• Combinatorial Optimization: Polyhedra and Efficiency, Vol. A,B,C, Schrijver
• Combinatorial Optimization: Algorithms and Complexity, Papadimitriou, Steiglitz
• Integer and Combinatorial Optimization, Wosley
• Convex Analysis and Optimization, Bertsekas

Complexity, Information and Coding

• Elements of Information Theory, Cover, Thomas
• An Introduction to Computational Learning, Kearns, Vazirani
• An Introduction to Kolmogorov Complexity and Its Applications, Li, Vit
• The Theory of Group Characters and Matrix Representations of Groups, Littlewood
• Representation Theory: A First Course, Fulton, Harris
• Introduction to Commutative Algebra, Atiyah, MacDonald
• Linear Representations of Finite Groups, Serre

Combinatorics

• Circuits of the Mind, Valiant
• Additive Combinatorics, Tao
• Combinatorial Problems and Exercises, Lovasz
• Enumerative Combinatorics, Vols. 1 & 2, Stanley

Analysis

• Real Analysis, Royden
• Real and Complex Analysis, Rudin
• Functional Analysis, Rudin
• Functional Analysis, Lax
• Functional Analysis, Yoshida
• Complex Analysis, Ahlfors
• Conformal Mapping, Nehari
• Fourier Analysis on Groups, Rudin

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