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# The Simplest Road—Direct Proofs

## Lecture no. 6 from the course: Prove It: The Art of Mathematical Argument

Taught by Professor Bruce H. Edwards | 30 min | Categories: The Great Courses Plus Online Mathematics Courses

Begin a series of lectures on different proof techniques by looking at direct proofs, which make straightforward use of a hypothesis to arrive at a conclusion. Try several examples, including proofs involving division and inequalities. Then learn tricks that mathematicians use to make proofs easier than they look.

## 24 Lectures

1

What Are Proofs, and How Do I Do Them?

0 of 31 min

2

The Root of Proof—A Brief Look at Geometry

0 of 30 min

3

The Building Blocks—Introduction to Logic

0 of 30 min

4

More Blocks—Negations and Implications

0 of 30 min

5

Existence and Uniqueness—Quantifiers

0 of 30 min

6

The Simplest Road—Direct Proofs

0 of 30 min

7

Let’s Go Backward—Proofs by Contradiction

0 of 30 min

8

Let’s Go Both Ways—If-and-Only-If Proofs

0 of 31 min

9

The Language of Mathematics—Set Theory

0 of 30 min

10

Bigger and Bigger Sets—Infinite Sets

0 of 32 min

11

Mathematical Induction

0 of 30 min

12

Deeper and Deeper—More Induction

0 of 31 min

13

Strong Induction and the Fibonacci Numbers

0 of 30 min

14

I Exist Therefore I Am—Existence Proofs

0 of 31 min

15

I Am One of a Kind—Uniqueness Proofs

0 of 30 min

16

Let Me Count the Ways—Enumeration Proofs

0 of 31 min

17

Not True! Counterexamples and Paradoxes

0 of 29 min

18

When 1 = 2—False Proofs

0 of 31 min

19

A Picture Says It All—Visual Proofs

0 of 31 min

20

The Queen of Mathematics—Number Theory

0 of 28 min

21

Primal Studies—More Number Theory

0 of 31 min

22

Fun with Triangular and Square Numbers

0 of 30 min

23

Perfect Numbers and Mersenne Primes

0 of 30 min

24

Let’s Wrap It Up—The Number e

0 of 31 min

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