transition to advanced mathematics

0:01:22

Prove that the union among sets is commutative.

0:57:01

Transition to Advanced Math: 16 Combinatorics I 57 min

0:03:33

A Transition to Higher Mathematics: 03 Intro to Logic

0:46:09

Transition to Advanced Math: 08 Proof Techniques I Introduction 46 min

0:50:04

Transition to Advanced Math: 24 Partially Ordered Sets I 50 min

0:08:39

Transition to Advanced Mathematics: Proof by Contrapositive

0:01:26

Prove that for any set A, AX(emptyset)=emptyset.

0:04:22

Prove one of De Morgan's Laws for Sets.

0:04:19

De Morgan's Laws for Families of Sets

0:03:36

2.1.12 Prove that X=Y, where X={x∈N:x^2 less than 30} and Y={1,2,3,4,5}.

1:02:52

Transition to Advanced Math: 15 Mathematical Induction II 62 min

0:09:08

Transition to Advanced Mathematics: Proof by Contradiction

0:05:13

2.1.7 True or false? (a) ∅∈P({∅,{∅}}) (b) {∅}∈P({∅,{∅}}) (c) {{∅}}∈P({∅,{∅}}) (d) ∅⊆P({∅,{∅}}) ...

0:53:52

Transition to Advanced Math: 09 Proof Techniques II Direct Proofs 54 min

0:22:30

Transition to Advanced Math: 11 Additional Proofs 23 min

0:02:40

A Transition to Higher Mathematics: 06 - Truth Tables

0:47:21

Transition to Advanced Math: 29 Cardinality III 47 min

0:35:26

Transition to Advanced Math: 18 Combinatorics III 35 min

0:41:28

Transition to Advanced Math: 22 Binary Relations II 42 min

0:36:51

Transition to Advanced Math: 13 Sets and Multisets II 37 min

0:03:55

2.1.10 Suppose that X={x:x∈R and x is a solution to x^2-7x+12=0} and Y={3,4}. Prove that X=Y.

0:11:47

2.3.16 Suppose A = {Ai:i∈N} is a family of sets such that for all i, j ∈N, if i ≤ j, then Aj ⊆ Ai.

0:11:32

Pursuing Advanced Mathematics

0:39:27

Transition to Advanced Math: 06 Predicate Calculus 39 min