# Math 4130-5130, Fall 2023

**Announcements****Test #1 will***be handed back on Monday, October 2. Remember that we will will not have class in-person the week of 9/25. I will be recording lectures and posting them to this site. I will email you all when the videos are available.***Course Information**

syllabus**Lecture Notes**

Lecture 3 (background on sets, operations, real scalar products) [August 28]

Lecture 4 (fields) [August 30]

Lecture 5 (intro to vector spaces) [September 6]

Lecture 6 (subspaces) [September 11]

Lecture 7 (linear combinations and span) [September 13]

Lecture 8 (linear independence)[September 25] LECTURE VIDEO**Review of Logic and Proofs**

Introduction to propositional logic (propositions, semantics, syntax, and logical operators)

More propositional logic (negations, tautologies, contradictions, logical equivalence, translations)

Introduction to predicate logic (one-place predicates, quantifiers, semantics, syntax, free variables)

Introduction to predicate logic II (as above but for n-place predicates)

More predicate logic (negations, translations, logical equivalence)

Conclusion of predicate logic (more translations and determination of truth)

Intro to proofs I (direct proofs and proof by contraposition)

Intro to proofs II (proof by contradiction, more examples)

Intro to proofs III (proofs of equivalences, proof by cases)

Intro to proofs IV (existential proofs, disproofs)

Introduction to sets (definitions)

Proofs with sets

Induction**Homework Assignments**

Homework #1 Solutions

Homework #2 Solutions

Homework #3 Solutions

Homework #4 Solutions

Homework #5 *(partial assignment – due by Sunday, October 1)***Test Solutions**