Foundations of Discrete Math: From Logic to Algorithms

Foundations of Discrete Math: From Logic to Algorithms
Published 4/2025
Duration: 3h 44m | .MP4 1280×720, 30 fps(r) | AAC, 44100 Hz, 2ch | 807 MB

Master sets, logic, proofs, combinatorics, and relations – the core of mathematical reasoning.

What you’ll learn
– Set Theory: Understanding sets, subsets, operations, and applications.
– Logic: Propositional and predicate logic, logical connectives, truth tables, and logical equivalence
– Proof Techniques: Direct proofs, proof by contradiction, and mathematical induction.
– Recursion and Sequences: Defining sequences recursively and solving recurrence relations.
– Asymptotic Analysis: Big O notation and analyzing algorithm efficiency.
– Combinatorics: Counting principles, permutations, combinations, and the pigeonhole principle.
– Probability: Basic probability theory, including conditional probability and Bayes’ theorem.
– Boolean Algebra: Boolean functions, logic gates, and applications in digital circuits.

Requirements
– Logical thinking – No formal logic experience required, but a willingness to think step-by-step is important.
– Curiosity and persistence – Some topics can be abstract, so an open mind and a bit of patience will go a long way!
Description
This course is modeled after a traditional university-level summer syllabus, but reimagined with flexibility and clarity for online learners. Through video lectures, thoughtfully designed problems, and a clear progression of topics, you’ll gain a robust understanding of discrete math – the backbone of logical thinking and algorithmic reasoning. Each lecture includes a detailed PDF resource with the descriptions, formulas, and key takeaways of the lecture.But much more broadly, this course is intended to teach you tothink mathematically. You may be a student who has never seen any math beyond calculus or algebra, or perhaps you dread doing math. The point of this course is to get you to learn to think deeply, communicate carefully, and not shy away from difficult material. The topics in this course are fundamental for students pursuing computer science, mathematics, or related fields, providing the necessary background for advanced studies.

As you proceed, have something to write with on hand. Work each example along with the course. Then, at the end of each chapter, work the exercises provided for you as PDFs. Some are more difficult than others, but are well worth doing to improve your understanding. Work along with someone at roughly your skill level, share solutions and ask each other questions.

Whether you’re preparing for computer science courses, diving into theoretical concepts, or strengthening your math fluency, this course equips you with the tools to think analytically and solve problems efficiently.

Who this course is for:
– Undergraduate students in computer science, mathematics, engineering, or related fields taking or preparing for a discrete math course.
– Aspiring developers who want a solid foundation in logic, proofs, and counting techniques essential for algorithms and programming.
– Self-paced learners looking to strengthen their mathematical thinking without needing advanced prerequisites.
– Curious minds interested in learning how formal logic, sets, and combinatorics work behind the scenes in tech and theory.
– CS and tech interview candidates preparing for algorithm-heavy roles or graduate-level theoretical computer science.
More Info

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