Lecture

Logic and Proof Techniques

Related lectures (26)

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Introduction to Mathematics for Engineers

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Closure Conversion: Representation and Transformation

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Integers and Rings

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Prime Numbers: Finding and Testing

Covers the definition of a function to determine if a given number is prime.

Introduction to Analysis

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Rational Numbers: Construction and Properties

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.