Discrete Mathematics 1

What you'll learn in this Udemy Course

• ✓ How to solve problems in chosen Discrete-Mathematics topics (illustrated with 395 solved problems) and why these methods work, step by step.
• ✓ Elementary Logic, including proving tautologies that involve implications, conjunctions, and disjunctions; necessary and sufficient conditions.
• ✓ Elementary Set Theory, including working with intersections and unions of sets, and other set-related topics.
• ✓ An introduction to mathematical theories, with concepts like axiom, theorem, primitive notion, etc.
• ✓ The concept of function between two discrete sets: injections, surjections, bijections.
• ✓ The concept of (a binary) relation as a subset of Cartesian product of two sets: RST relations, order relations, etc.
• ✓ RST relations and the concept of equivalence classes; an illustration for a modulo relation between integers.
• ✓ Functions as relations; various ways of depicting functions between two discrete sets; equipotent sets.
• ✓ An introduction to the topic of sequences, only basic concepts that can be needed in Combinatorics; we come back to the topic of sequences in DM3.
• ✓ Various proof techniques, including direct proofs, proofs by contradiction, proofs by contrapositive, Mathematical Induction, and Pigeonhole Principle.
• ✓ A preparation for Combinatorics: the concept of index, the sigma sign (with computational rules), n factorial, n choose k, Pascal's Triangle, Binomial Theorem.
• ✓ A brief introduction to Combinatorics: the art of counting. Permutations, combinations, paths, etc; the topic will be continued in the first sections of DM2.
• ✓ Playful logical problems and riddles, including the famous Zebra Puzzle (Einstein's Riddle), and some classical riddles about liars and truth tellers.
• ✓ This is the first course in Discrete Mathematics, so don't worry that neither Number Theory nor Graph Theory are covered; they will be covered in a sequel.