Modules Topics covered in this class.

This page presents the “modules”, or the topics that are covered in this course.

Click on the tile associated with a module to go to a page containing that module’s contents.

1. Propositional Logic

Assertions and propositions, connectives, tautologies, contradictions, implications, equivalences, proofs.

2. Predicate Logic

Predicates, quantifiers, free and bound variables, implications, equivalences, inference rules, proof techniques.

3. Sets

Sets, set notation, relationships between sets, set operations, set properties, proving set properties, Russell’s Paradox.

4. Functions

Operations on functions, classification of total functions, cardinality, set membership, logarithms, exponentiation.

5. Linear algebra

Applications of linear algebra, systems of linear equations, gaussian elimination with back substitution, Gauss-Jordan elimination, Cramer’s Rule.

6. Sequences, series, summations

Sequences, recurrence systems, series, generating functions.

7. Data representations

Positional number systems (binary, octal, hexadecimal), natural numbers, signed integers, floating point, characters.

8. Algorithms

Algorithms, computational complexity, asymptotic notations, pseudocode, greedy algorithms, easy vs. hard problems.

9. Number theory

Number theory, least common multiple (LCM), greatest common divisor (GCD), primes, factorization, congruences, modular arithmetic.

10. Induction and recursion

Inductive definitions, recurrence systems, proof by induction, recursive algorithms, recursion vs. iteration.

11. Counting

Combinatorics, permutations, combinations, selections, pigeonhole principle, inclusion-exclusion.

12. Discrete probability

Probability theory, computing discrete probabilities, random variables, discrete distribution functions, Bayes’ Theorem, expected values, Central Limit Theorem.