Syllabus:
Logic and set theory. Introduction to proofs, axiomatic method, proof patterns. Well ordering principle. Logical formulas  propositional and predicate. Sets, relations, equivalences and partial orders. Induction. Recursive definitions. Infinite Sets: Cantor’s theorem, diagonalization argument, halting problem. Logic of sets. [12 lectures + 4 tutorial sessions ]
Graph Theory. Graphs, degree. Common graphs. Walks, paths, connectivity, cycles, trees, forests. Cliques, Independent sets. Graph Isomorphism, bipartite graphs and matchings. Colouring. Planar graphs: Euler’s formula, 6colouring of planar graphs. Regular polyhedra. [8 lectures + 3 tutorial sessions]
Combinatorics. Product rule, division rule, counting subsets, sequences with repetitions  binomial and multinomial theorems. Pigeonhole principle. Inclusionexclusion. Combinatorial proofs. Twelvefold way. Recurrence relations  Fibonacci numbers and Towers of Hanoi puzzle. [8 lectures + 3 tutorial sessions]
Discrete Probability. Events and probability spaces, The four step method, birthday principle. Set theory and probability. Conditional probability, law of total probability. Independence. Probability versus confidence. Random variables: independence. distribution functions, expectations. Linearity of Expectation [14 lectures + 4 tutorial sessions]
Learning Outcomes

Use logical notation to define and reason about fundamental mathematical concepts such as sets, relations, functions, and integers.

Evaluate elementary mathematical arguments and identify fallacious reasoning (not just fallacious conclusions).

Synthesize new proofs based on standard proof patterns.

Apply graphtheoretic models to solve problems like job allocation, scheduling, connectivity etc.

Calculate numbers of possible outcomes of elementary combinatorial processes such as permutations and combinations.

Calculate probabilities and discrete distributions for simple combinatorial processes; calculate expectations.
Textbook
 Mathematics for Computer Science. Eric Lehman, F Thomson Leighton, Albert R Meyer. This book is available online under the terms of the Creative Commons Attribution ShareAlike 3.0 license. URL Printed version: 12th Media Services. ISBN13: 9781680921229.
Reference

Discrete Mathematics and Applications. Kenneth Rosen (7th Edition, 2012), McGrawHill Education (ISBN13: 9780073383095)

Invitation to Discrete Mathematics. Jiří Matoušek and Jaroslav Nešetřil (2nd Edition) Oxford University Press (ISBN13: 9780198570424)

Discrete Mathematics: Elementary and Beyond. László Lovász, József Pelikán, Katalin Vesztergombi, Springer 2003, ISBN13: 9780387955858.
Popular Readings

Logicomix: An epic search for truth. Apostolos Doxiadis and Christos Papadimitriou. Bloomsbury USA. ISBN13: 9781596914520

What is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles. Raymond M. Smullyan. Dover Publications.
ISBN13: 9780486481982

Proofs from THE BOOK. Martin Aigner and Günter M. Ziegler. Springer. ISBN13 : 9783642008559
 Combinatorics: A Very Short Introduction. Robin Wilson. Oxford University Press. ISBN13 : 9780198723493
Notes
 This course is modelled along the Mathematics for Computer Science course (6.042J, Spring 2015) at MIT.