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