Math 109, Fall 2019

Math 109 - Mathematical Reasoning (4 units), Fall 2019

Lecture: MWF 10am-10:50am in 001 Cognitive Science Building
Discussion:
- (E01) M 5pm-5:50pm in 2402 AP&M
- (E02) M 6pm-6:50pm in 2402 AP&M
- (E03) M 7pm-7:50pm in 203 Center Hall
Course Description: This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs. Required of all departmental majors.
Prerequisites: Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed listed prerequisites may enroll with consent of instructor.
Textbook: An Introduction to Mathematical Reasoning by Peter J. Eccles
Homework: Problem sets will be due roughly every week on Thursdays by 4pm in the AP&M homework dropbox located in the basement. Links to the assignments will appear in the schedule below. No homework scores will be dropped. An assignment may be submitted late by the following Monday at 2pm, but it will earn a maximum of 75% of its total score.
Exams:
- Midterm Exam 1: Wednesday, October 23 in class
- Midterm Exam 2: Wednesday, November 20 in class
- Final Exam: Friday, December 13, 8am-11am in our usual classroom
Homework and Exam Policies: No cell phones, calculators, notes, books, or any other form of assistance are allowed during exams. Once homework is returned, the instructor or TA must be contacted within a week of this date if there was a mistake made in grading. No grade changes will be made after this day. Once exams are returned, you must return your exam immediately to your TA in order to request a regrade. Include a written explanation stating which problem(s) you would like regraded and why. Regrade requests will not be considered once the exam leaves the room. If you do not retrieve your exam during discussion, you must arrange to pick it up from your TA within one week after it was returned in order for any regrade requests to be considered. Work will be graded for both clarity and correctness. No make-up exams will be given.

Grading: Homework and exam grades will be posted on TritonEd. Final grades will be calculated as the maximum of the following two grading schemes and using the following table:

20% Homework, 20% Midterm Exam 1, 20% Midterm Exam 2, 40% Final Exam
20% Homework, 20% Best Midterm Exam Score, 60% Final Exam

A+	A	A-	B+	B	B-	C+	C	C-	D	F
97	93	90	87	83	80	77	73	70	60	<60

Instructor Information:
- Leesa B. Anzaldo
  - lbanzaldo@ucsd.edu
  - Office Hours: MW 9am-9:45am and MWF 1pm-2pm in 6311 AP&M
TA Information:
- (E01, E02) Alexander Mathers
  - amathers@ucsd.edu
- (E03) Jason O'Neill
  - jmoneill@ucsd.edu
  - Office Hours: Mondays 4pm-5pm in 5218 AP&M, and Thursdays 11am-12pm in 5829 AP&M
Piazza: In addition to going to office hours and forming study groups, students can get help by posting questions/answers here. Full solutions to homework problems may not be posted before the due date.
Academic Accommodations: Students requiring accommodations should provide an OSD letter of certification and OSD accommodation recommendation to the instructor as soon as possible.
Classroom Behavior and Academic Integrity: All members of class should be respectful of one another at all times. Academic dishonesty will not be tolerated. Click here for information on how to promote academic integrity and the consequences of cheating.

Homework and Tentative Schedule


Sep 27	Ch. 1 - The language of mathematics
Sep 30	Ch. 2 - Implications
Oct 2	Ch. 3 - Proofs
Oct 4	Ch. 4 - Proof by contradiction

Oct 7	Ch. 4 - Proof by contradiction (continued), Ch. 5 - The induction principle
Oct 9	Ch. 5 - The induction principle (continued)
Oct 10	HW 1 due, Solutions
Oct 11	Ch. 6 - The language of set theory

Oct 14	Ch. 6 - The language of set theory (continued), Ch. 7 - Quantifiers
Oct 16	Ch. 7 - Quantifiers (continued), Ch. 15 - The division theorem
Oct 17	HW 2 due, Solutions
Oct 18	Ch. 15 - The division theorem (continued), Ch. 16 - The Euclidean algorithm

Oct 21	Review, Practice problems, Solutions
Oct 23	Midterm 1
Oct 25	Ch. 8 - Functions

Oct 28	Ch. 8 - Functions (continued), Ch. 9 - Injections, surjections, and bijections
Oct 30	Ch. 9 - Injections, surjections, and bijections (continued)
Oct 31	HW 3 due, Solutions
Nov 1	Ch. 10 - Counting

Nov 4	Ch. 10 - Counting (continued), Ch. 11 - Properties of finite sets
Nov 6	Ch. 11 - Properties of finite sets (continued), Ch. 12 - Counting functions and subsets
Nov 7	HW 4 due, Solutions
Nov 8	Ch. 12 - Counting functions and subsets (continued)

Nov 11	No class
Nov 13	Ch. 13 - Number systems
Nov 14	HW 5 due, Solutions
Nov 15	Ch. 13 - Number systems (continued), Ch. 14 - Counting infinite sets

Nov 18	Review, Practice problems, Solutions
Nov 20	Midterm 2
Nov 22	Ch. 14 - Counting infinite sets (continued)

Nov 25	Ch. 14 - Counting infinite sets (continued), Ch. 19 - Congruence of integers
Nov 27	Ch. 19 - Congruence of integers (continued), Ch. 22 - Partitions and equivalence relations
Nov 29	No class

Dec 2	Ch. 22 - Partitions and equivalence relations (continued)
Dec 3	HW 6 due by 1pm, Solutions
Dec 4	Ch. 23 - The sequence of prime numbers
Dec 6	Review, Practice problems, Solutions

Dec 13	Final Exam: 8am-11am in 001 Cognitive Science Building