Udemy – Discrete Mathematics 1 2025-5

Discrete Mathematics 1. This course covers the basic topics of this branch of mathematics and provides a foundation for understanding more advanced concepts. The course covers introductory concepts to academic topics and is divided into fourteen sections. In the first section, participants are introduced to the course structure and study method. The second section teaches basic principles such as proving formulas, divisibility, and problem-solving methods. The third section deals with logic and introduces logical symbols, suras, and necessary and sufficient conditions. The fourth section covers set theory and examines concepts such as union, commonality, and cardinality. The fifth section is devoted to functions and explains types of functions, their domain, range, and composition. The sixth section teaches binary relations, equivalence, and ordinal relations. The seventh section defines functions as special relations. The eighth section provides a brief introduction to sequences. Part 9 examines various proof techniques such as direct, indirect, and induction proofs. Part 10 introduces the concepts of factorials, binomial coefficients, and the binomial theorem. Part 11 covers the principles of combinatorics, permutations, and counting. This course is the first in a trilogy, and more advanced topics such as number theory, graphs, and probability will be covered in later courses (DM2 and DM3).

What you will learn

• How to solve problems in selected discrete mathematics topics (with 395 solved problems) and why these methods work, step by step.
• Elementary logic, including proofs of equivalences involving implication, inflection, and division; necessary and sufficient conditions.
• Elementary set theory, including work with the intersection and union of sets and other set-related topics.
• An introduction to mathematical theories, with concepts such as axioms, theorems, basic concepts, etc.
• The concept of a function between two discrete sets: one-to-one, spanning, and bidirectional functions.
• The concept of a (binary) relation as a subset of the Cartesian product of two sets: RST relations, order relations, etc.
• RST relations and the concept of equivalence classes; an explanation for the moduli relation between integers.
• Functions as relations; different ways of representing functions between two discrete sets; equipotent sets.
• An introduction to the topic of sequences, just the basic concepts that may be needed in combinatorics; we will return to the topic of sequences in DM3.
• Various proof techniques, including direct proofs, proof by contradiction, proof by contradiction, mathematical induction, and the pigeonhole principle.
• Preparation for combinatorics: concept of index, sigma sign (with calculation rules), n factorial, n choice of k, Pascal’s triangle, binomial theorem.
• A brief introduction to combinatorics: the art of counting. Permutations, combinations, paths, etc.; this topic will be continued in the first parts of DM2.
• Fun logic problems and riddles, including the famous zebra riddle (Einstein’s riddle) and some classic 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 is covered; they will be covered in later courses.

This course is suitable for people who:

• Students who plan to study mathematics at the college or university level and want to achieve mathematical maturity for success.
• High school students who are curious about academic mathematics; this course is intended for purchase by adults.
• Anyone who wants to review their high school math and gain a deeper understanding of the subject.
• College and university students studying advanced courses who want to understand all the details they may have missed in their previous training.
• Students who need mathematics for computer science, artificial intelligence, machine learning, or other fields that require mathematics.