# Math 3410, Fall 2022

**Announcements***The final exam will be held on Thursday, December 15 from 3-6 pm.***Course Information**

syllabus**Lecture Notes**

August 22 – review of logic (see first 6 PDFs below)

August 24 – review of proofs and sets (see final 7 PDFs below)

August 29 – introduction to the real numbers: algebraic axioms

August 31 – consequences of algebraic axioms, intro to natural numbers

September 7 – the integers and the rational numbers (**updated on 9/9**)

September 12 – introduction to order axioms

September 14 – absolute value and completeness

September 19 – exponents and more completeness

September 26 – even more completeness, introduction to sequences

September 28 – more on sequences: convergence to 0

October 10 – further results on sequences converging to 0

October 12 – completion of limit laws for sequences converging to 0, intro to general limits

October 17 – general limit laws

October 19 – finishing up limit laws

October 24 – Cauchy sequences

October 26 – finishing up sequences

October 31 – introduction to series

November 2 – alternating series, absolute convergence, ratio test

November 7 – more series tests

November 9 – intro to functions

November 21 – intro to limits of functions

November 28 – more limits of functions

November 30 – introduction to continuity (Extreme Value Theorem)

December 5 – Intermediate Value Theorem **Videos**

Introduction to the course

August 22

August 24

August 29

August 31

September 7

September 12

September 14

September 19

September 21

September 26

September 28

October 3 (** review for Test 1**)

October 10

October 12

October 17

October 19

October 24

October 26

October 31

November 2

November 7

November 9

November 14 (

**)**

*review for Test 2*November 21

November 28

November 30

December 5

**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 Solutions

Homework #6 Solutions

Homework #7 Solutions

Homework #8 Solutions

Homework #9 Solutions

Homework #10 Solutions

Homework #11 Solutions

Homework #12 Solutions

Homework #13 Solutions

Homework #14 Solutions

**Test Solutions**

Test #1 Solutions

Test #2 Solutions