**Math 109 - Mathematical Reasoning**

**Winter 2023**

**Instructor: **Daniel Vallieres

**Lectures: **MWF 1:00-1:50

**Where: **~~PETER 102~~ WLH 2205

**Office hours: **MWF 2:30-3:30

**Office:** AP&M 1220

**Email:** dhvallieres at ucsd dot edu

**Teaching assistant for Section C01: **Jacob Keller

**Discussion sections:** C01 T 8:00-8:50 in AP&M 2301

**Office hours:** Th 3:30-5:30

**Office: ** HSS 4008

**Emails:** jjkeller at ucsd dot edu

**Teaching assistant for Section C0****2****: **Nathan Conlon

**Discussion sections:** C02 T 9:00-9:50 in AP&M 2301

**Office hours:** M 5:00-7:00

**Office:** AP&M 2313

**Emails:** nconlon at ucsd dot edu

**Description: **Among all of scientific disciplines, mathematics hold a special place. Starting with Euclid's *Elements* in 300 B.C., mathematicians developed a rigorous way to communicate mathematical truths to one another based on the *axiomatic method* and *formal logic*. As a results, most books in mathematics are terse and hard to read as you probably noticed already by looking at some calculus books. Do you remember the format: Definition - Theorem - Proof, Definition - Theorem - Proof, etc??? And have you ever asked yourself why mathematics books are written this way?

This course will introduce the students to *rigorous mathematical proofs* and the *basic language* (naive set theory) used by every mathematician to communicate mathematical results in a precise way. Topics to be covered include: logic and the use of quantifiers, naive set theory, functions, relations and equivalence relations, methods of proof such as direct proof, proof by contradiction, proof by contrapositive, proof by cases, induction, and counterexamples. The goal is to cover parts of the first 22 chapters in your book.

**Canvas: ** All announcements for this course will be made in Canvas. It is your responsibility to check Canvas often or to set up your notifications to your own liking for not missing an announcement. I will also post the grades in Canvas. You can access Canvas by clicking here.

**Book:** *An Introduction to Mathematical Reasoning* by Peter J. Eccles

**Exams:** There will be two midterms given in class:

Wednesday, February 1, 1:00 - 1:50 in WLH 2205

Wednesday, March 1, 1:00 - 1:50 in WLH 2205

I will announce later when and where the final exam will be. *No notes, textbooks, calculators are allowed during exams. No make-up exams will be given.*

**Reading:** You will get the most out of this class if you read the book carefully on your own. Every week, I will let you know which chapter in the book you should read.

**Homework assignments: **There will be weekly homework assignments. ~~You will have to submit your hw assignments to your teaching assistant during your discussion section~~. You will have to submit your assignment in Gradescope on Tuesday before 8am. The first homework assignment will be due on January 17. Only a sample of the problems you submit will be graded, but you will not know which ones ahead of time.

**Help options:** I strongly encourage you to go to your discussion sections. This will be your opportunity to ask questions about the lectures, the hw problems that have not been graded or any hw problem you have been struggling with. On the other hand, you are welcome to come to my office hours or to your TAs' office hours to ask any questions about the hw problems prior to the deadline. The TAs and myself will try to give you hints if you are stuck and not sure how to attack one particular problem. I encourage you to work with classmates on homework problems, but you have to submit your own copy that reflects your own understanding.

**Grading policy:** Homework assignments will be worth 20%, midterm 1 20%, midterm 2 20%, and the final exam 40%. I guarantee that 93% will be an A, 90% will be an A-, 87% a B+, 83% a B, 80% a B-, 77% a C+, 73% a C, 70% a C- and above a 60% a D. I also guarantee that 60% or above is a pass.

In order to encourage you to go to your discussion section, if you go to 80% or more of the discussion sections throughout the quarter, you will get a 5% for free on your final grade for participation, and your final exam will count for only 35% rather than 40% of your final grade.

**Accommodations:** Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter (paper or electronic) issued by the Office for Students with Disabilities (https://osd.ucsd.edu) Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department **in advance** of any exams or assignments

**Academic Integrity:** Academic integrity is highly valued at UCSD and academic dishonesty is considered a serious offense. Students involved in an academic integrity violation will face an administrative sanction which may include suspension or, in very serious cases, expulsion from the university. Your integrity has great value: Cultivate and protect your academic integrity.

**Schedule**

This is a tentative schedule and I reserve the right to change it if need be.

**Week 1 (01/09)**:

Monday: We will go over the syllabus, and we will try to motivate the need for rigorous mathematical proofs via Polya's conjecture.

Wednesday: Chapter 1: The language of mathematics.

Friday: Chapter 1: The language of mathematics; Chapter 2: Implications.

**Week ****2 (01/16)**:

Monday:

**Martin Luther Kin****g Jr Holiday - No class**Wednesday: Chapter 2: Implications.

Friday: Chapter 3: Proofs

**Week ****3 (01/23)**:

Monday: Chapter 4: Proofs by contradiction.

Wednesday: Chapter 4: Proofs by contradiction. Proofs by contrapositive.

Friday: Chapter 5: Proofs by induction.

**Week ****4 (01/30)**:

Monday: Chapter 5: Proofs by induction

Wednesday:

*Midterm 1*Friday: Chapter 6: The language of set theory

**Week ****5 (02/06)**:

Monday:

Wednesday:

Friday:

**Week ****6 (02/13)**:

Monday:

Wednesday:

Friday:

**Week ****7 (02/20)**:

Monday:

**Presi****dents' day Holiday - No class**Wednesday:

Friday:

**Week ****8 (02/27)**:

Monday:

Wednesday:

*Midterm 2*Friday:

**Week ****9 (03/06)**:

Monday:

Wednesday:

Friday:

**Week 10 (03/13)**:

Monday:

Wednesday:

Friday: