Adam Panagos / Engineer / Lecturer
Mathematical Proofs
Course Description
This is an undergraduate course in deductive reasoning that teaches students general strategies for developing their own rigorous proofs. Important course concepts include basic concepts from set theory (e.g. set union, intersection, power set, indexed families of set), different proof strategies (direct, contradiction), relations, and functions.
The course material and pace make this a challenging undergraduate course. To help my students I developed my own set of example video problems to provide them more examples to study. See the comprehensive collection of example problems below. This collection consists of 55 videos totaling ~6 hours of content.
The textbook used for the course is, "How To Prove It: A Structured Approach", 2nd edition by Daniel J. Velleman.
Another excellent resource for this type of material is, "The Book of Proof" by Richard Hammack.
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Example Problems

Logical Connectives (3 videos, ~18 minutes)

Truth Tables (2 videos, ~14 minutes)

Logical Expression Simplification (3 videos, ~14 minutes)

Sets (5 videos, ~32 minutes)

Conditional Connectives (1 video, ~6 minutes)

Quantifiers (6 videos, ~ 36 minutes)

More Sets (4 videos, ~23 minutes)

Direct Proofs (3 videos, ~17 minutes)

Contradiction Proofs (2 videos, ~10 minutes)

IfAndOnlyIf Proofs (4 videos, ~25 minutes)

Family of Sets and Indexed Family of Sets (3 videos, ~17 minutes)

Cartesian Products (2 videos, ~13 minutes)

Relations and Partial Orders (7 videos, ~55 minutes)

Functions (6 videos, ~36 minutes)

Induction (4 videos, 25 minutes)