# Math 3410, Fall 2023

**Announcements***The final exam will be held Monday, December 11 from 12:40-2:40 pm. The final will be comprehensive, but 40% of the exam will be taken directly from homework and the three tests.***Course Information**

syllabus**Lecture Notes**

Lecture 3 (algebraic axioms for the real numbers) [August 28]

Lecture 4 (some consequences of the algebraic axioms) [August 30]

Lecture 5 (order axioms (all but completeness)) [September 6]

Lecture 6 (absolute value and completeness) [September 11]

Lecture 7 (more completeness) [September 13]

Lecture 8 (consequences of completeness, intro to sequences)[September 25] LECTURE VIDEO

Lecture 9 (more on sequences: convergence to 0) [September 27] LECTURE VIDEO

Lecture 10 (more on convergence to 0; limit laws for sequences) [October 2]

Lecture 11 (more limit laws, Squeeze Theorem, intro to general limits of sequences) [October 4]

Lecture 12 (some general limit laws) [October 9]

Lecture 13 (more limits) [October 11]

Lecture 14 (Cauchy sequences) [October 23]

Lecture 15 (finishing up sequences: more Cauchy sequences, contractive sequences) [October 25]

Lecture 16 (introduction to series) [October 30]

Lecture 17 (more series tests) [November 6]

Lecture 18 (even more series tests) [November 8]

Lecture 19 (intro to limits of functions) [November 27] *[Note – there are a few minor typos in this set of notes which I will point out in class; I lost the source code for this lecture, and since the typos are very minor, I deemed it not worth it to retype]*

Lecture 20 (more limits of functions) [November 29]**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 *(complete assignment) Due by Wednesday, December 6 at 11:59 pm*

Homework #11 Solutions**Test Solutions**

Test 1 Solutions

Test 2 Solutions

Test 3 Solutions