MATH 109

Mathematical Reasoning

Lecture C00, Fall 2020

CANVAS

Course materials and Zoom links will be posted on CANVAS.

Instructor

Teaching Assistant

Textbook

This is an excellent free textbook. We will cover most of the content in Chapters 1, 2, 4-12 and (time permitting) part of Chapter 13.

Grading

Your percentage grade in the course is calculated to be the higher of the following two grading schemes:

  • 20% Homework + 40% Quizzes (10% Each) + 40% Final Exam

  • 20% Homework + 30% Quizzes (10% for each of best 3 quizzes, 0% for worst quiz) + 50% Final Exam


This course is "curved" in the sense that precise grade cutoffs are determined at the end of the quarter. However, the following guidelines will be followed.

  • The course median will be at least a B-.

  • Your grade will be at least as high as guaranteed by the department's standard grade cutoffs:

    • 95% guarantees a grade of at least an A+

    • 90% guarantees a grade of at least an A

    • 85% guarantees a grade of at least an A-

    • 80% guarantees a grade of at least a B+

    • 76% guarantees a grade of at least a B

    • 72% guarantees a grade of at least a B-

    • 68% guarantees a grade of at least a C+

    • 64% guarantees a grade of at least a C

    • 60% guarantees a grade of at least a C-

Assignments

Assignments will be posted to Canvas and are to be submitted through Gradescope by 10 am. No late assignments will be accepted.

  • HW1 is due Friday, October 16

  • HW2 is due Friday, October 23

  • HW3 is due Friday, October 30

  • HW4 is due Friday, November 6

  • HW5 is due Friday, November 13

  • HW6 is due Friday, November 20

  • HW7 is due Friday, December 4

  • HW8 is due Friday, December 11

All assignments are equally weighted. If at least 60% of students fill out CAPEs at the end of the term, then the worst assignment will be dropped for each student.

Quizzes

Quizzes will be timed and available through Canvas. Additional details: TBA.

  • Quiz 1 is on Monday, October 26

  • Quiz 2 is on Monday, November 9

  • Quiz 3 is on Monday, November 23

  • Quiz 4 is on Monday, December 7

Final Exam

The final exam is cumulative. Details: TBA.

Regrade Policy

Following the return of each assignment and exam, there will be a window of time in which you may request a regrade. Regrade requests must be accompanied by a detailed explanation of why you believe there was a grading error.

Academic Integrity

Collaboration

You are allowed to discuss homework problems with your classmates. However, the final write-up of solutions should be your own work, and reflect your own understanding of the problems. Copying or paraphrasing part of the solution to a homework problem from a classmate or from the internet is considered academic dishonesty.

Academic Dishonesty

Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.

Exam/Quiz Cheating

Any cheating on quizzes or exams will result in an automatic F in the course plus administrative penalties. There will be no exceptions to this rule.

Assignment Cheating

Any assignment cheating will result in an automatic 0% in the homework category for this course plus administrative penalties. There will be no exceptions to this rule.

Students agree that by taking this course that student submissions may be subject to submission for textual similarity review to Turnitin.com for the detection of plagiarism. All submitted content will be included as source documents in the Turnitin.com reference database solely for the purpose of detecting plagiarism of such papers. Use of the Turnitin.com service is subject to the terms of use agreement posted on the Turnitin.com site.

List of Topics

  1. Foundational material

    • Sets (Chapter 1)

    • Logic (Chapter 2)

  2. Techniques of Mathematical Proof

    • Direct Proofs (Chapter 4)

    • Contrapositive Proofs (Chapter 5)

    • Proof by Contradiction (Chapter 6)

    • Mathematical Induction (Chapter 10)

  3. More on Mathematical Proofs

    • Proving Nonconditional Statements (Chapter 7)

    • Proofs Involving Sets (Chapter 8)

    • Disproof (Chapter 9)

  4. Fundamental Notions in Advanced Mathematics

    • Relations and Modular Arithmetic (Chapter 11)

    • Functions (Chapter 12)

    • Elements of Number Theory (Sections 5.2, 10.4, 11.5, and various results scattered throughout the textbook)

    • The precise definition of a limit (Sections 13.2-13.3)

In an ideal world, I would also cover basic topics from discrete mathematics (Chapter 3), cardinalities of sets (Chapter 14), and additional topics on analysis (Chapter 13) in this course. Unfortunately, covering these additional topics in addition to those listed above is not feasible in a single quarter.

All information on this webpage is subject to change. Students are responsible for checking this webpage regularly for updates.