**ANNOUNCMENTS:**

**Updates**(as of April 3)**Final Exam: The final exam will have two parts: a take home portion and a timed portion to take place on April 28 from 10 am – 11:45 am on Carmen. (Review-Final-Exam)**- Office hours, as well as meetings with Dennis and Elizabeth are to be conducted through Carmen Zoom, Carmen Discussion board, or email. Instructions will be send to you.
- Find the syllabus here.

- Welcome to Math 3345H. We will be working with mathematics and reasoning skills in new ways. Your success in this course will depend on participation, as well as making daily efforts to marinate yourself in the material outside of the classroom.

**HOMEWORK: **

You are encouraged to write your homework using LaTex. Here is a template as well as some additional help and here is a quick symbol reference.

Assignment_1_(logic) and Reading 1 (pigeon hole principle) (due Friday, January 10 at the 10:20 am in class (no late homework accepted)). *skip exercise 5 of assignment 1

Assignment 2 (logic) (pdf, tex) (due Wednesday, January 15 at the 10:20 am in class (no late homework accepted)).

Assignment 3 has three components (a) complete all even exercises from Chapter 1, section 3 (quantifiers) (b) watch video, (c) Read Examples 1 and 2 (pages 1-8) (due Wednesday, January 22 at the 10:20 am in class (no late homework accepted)).

Assignment 4 (divisibility, irrationals, primes) (pdf, tex ) (due Wednesday, January 29 at the 10:20 am in class (no late homework accepted)).

Assignment 5 (Induction, divisibility, primes well-ordering) (pdf) (due Wednesday, Feb 5 at the 10:20 am in class).

Instructions: **Part I**: Exercises 1-4, 6, 8, 19, 27 from the pdf. Bonus exercises: 10, 17, 21 **Part II**: Exercise 29, page 53 in your book. Read the first 3 pages in your book on Induction.

Assignment 6 (due Feb 14*** , NOTE: Due to Midterm last week, you have until Friday to turn in this assignment: Complete exercises 5, 13a from Chapter 2, section 5; exercises 2, 4 from section 6; exercise 5 from Number theory notes page 4; complete a Proof Journal entry for the Binomial Formula)

Assignment 7 (Bezout’s lemma, complete induction, set builder notation) (due **Feb 19** at the 10:20 am in class) Instructions: Complete a proof journal entry for Bezout’s lemma (see number theory notes page 9); Complete a proof journal entry for Theorem 7.4 (division by a prime); Complete the following exercises in your book: 7.4 (section 7, exercise 4), 10.4, 10.9)

Assignment 8 (set builder notation continued, Chinese Remainder Theorem ) (due Feb 26 at the 10:20 am in class) Complete the following exercises in your book: 10.13, 10.14, 10.16, 10.19, 10.24, 10.25; Complete Exercises 9 and 10 in this handout: set builder handout (pdf, tex) ); Complete a proof journal for this theorem (2.6.5).

Assignment 9 (pdf, tex) (due March 4 at the 10:20 am in class). Reading: Russel’s Paradox (wiki and youtube); Problems from Chapter 2 of the book: 4.26, 6.6 (part a), 6.7, 6.8, 6.10, 6.12, 10.15, 10.17, 10.18, 10.20; be familiar with handout from class; (*no proof journal this week- HW out of 30)

Assignment 10 (pdf, tex) (due March 25 at 10:20 am online…upload to Carmen under Assignment 10)

Assignment 11 (pdf, tex) (due April 3* at 10:20 am)

Assignment 12 (due April 8 at 10:20 am)(Chapt. 3, section 11, exercises 1, 3, 9, 12, 19, 21, 26; section 12, exercise 1 (see definition of graph in your book)). In addition to these exercises from the book, you should complete the attached proof journal assignment: pdf, tex)

Assignment 13 (pdf) (due April 15 at 10:20 am) This assignment has three parts and they should be UPLOADED SEPARATELY:

**Part I:**Exercises from the book: Chapter 3, section 12 (exercises: 16, 21, 28); section 13 (5, 13); section 14 (8)**Part II**: Exercises 1,2,3 (4 is bonus) from this handout from Dennis (Jensen’s inequality).**Part III**: Read Theorem 1 and the proof of Erdős (reading), Read background on this problem: Erdős (background), Using Wikipedia, understand the statement of both the Erdos distinct distance problem and the Erdos unit distance problem. Does one imply the other? (hint: pigeon hole) (you need not turn anything in yet for Part III)

Assignment 14 (pdf) (due April 22 at 10:20 am) Dennis gave his part of the assignment on Friday. Please see his slides here.

**PROOF JOURNAL INSTRUCTIONS: **Please look at all three documents below:

**BOOKS: **

The Fundamentals of Higher Mathematics, N. Falkner (official text for this course)

The Cauchy-Schwarz Master Class (Steele, free online)

Mathematics and Logic (Kac and Ulam, free online)

**HANDOUTS and READING:**

Part 2: Injective/ Surjective hand-out (plus Cauchy-Schwarz)

Part 1: Injective/ Surjective hand-out

set builder handout (pdf, tex)

Russel’s Paradox + Set builder hand-out

Proof using contrapositive, Proof by way of contradiction

More Number theory + Olympiad problems + Modular arithmetic

Erdős (background), Erdős (reading)

infinity handout plus equivalence relations

Functions: Injective Surjective handout

**Lectures Notes:**

- Monday, March 23: Cartesian products, functions
- Wednesday, March 25: functions continued (injective, surjective, functionals and power sets)
- Monday, March 30:bijections, inverses
- W, F April 1, April 3: (Chapter 3, Section 11 continued + Section 12)
- Monday, April 6: Counting and Combinatorics (Chapter 3, Section 13)
- Wednesday, April 8 Chapt 3, section 15 ( infinite sets part I)
- Friday, April 10: Dennis’s Presentation Jensen’s Inequality
- Monday, April 13+15: Chapt 3, section 15 ( infinite sets part II)
- Friday, April 17: cardinality (Dennis’s slides)
- Monday, April 20: Relations Apr 20, 2020

**Technology: **

- I found this useful for mirroring ipad and mac: https://youtu.be/TB0tGWbhF2E

**OFFICE HOURS and MENTORING (Tutoring): **

(We are very happy to help and to see you. Please feel free to come by anytime or e-mail to let us to set up an appointment: Elizabeth Campolongo ( her first lastname.4@osu.edu), K. Taylor (my last name.2952@osu.edu)

- Monday 2 pm – 4 pm (email or Carmen discussion board discussions, with Dennis Sweeny)
- Tuesday 5:10 – 6:10 pm (email or Carmen discussion board, with Elizabeth Campolongo)
- Saturday 12 pm – 2 pm (CarmenZoom, with Dennis Sweeny)

**MIDTERMS and REVIEW SESSIONS:**

- Midterm 1 Friday, February 7 (in class); See Midterm I review questions here
- Midterm 2 Friday, March 27 (online); See Midterm II review questions
**here.**

**Final Exam **

- Final Exam: Tuesday, April 28 (online. Due at 11:45 am)
**Review-Final-Exam**

**SYLLABUS: **

- Find the syllabus here.

**MATH READING AND VIDEOS** (more books and reading suggested in syllabus):

(found by Michael)

Fun math links (REUs, study abroad, what is math…)

pigeon hole principle (Meyer-2013)

please check back soon for some interesting mathematics and course updates…