Math 109 -- Mathematical Reasoning -- Winter 2018

Lecture site: CENTR 212
Lecture times: Monday, Wednesday, Friday. 11:00pm-11:50pm.
Discussion sessions B01 927126: Wednesday 4:00p-4:50p, AP&M B412 with Renee Mirka
B02 927127: Wednesday 5:00p-5:50p, AP&M B412 with Pieter Spaas
B03 927128: Wednesday 6:00p-6:50p, AP&M B412 with Pieter Spaas
Final Exam
time and place
March 19th, 2018, 11:30pm - 2:29pm. Place to be announced.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 5880E
Hours: Monday. 3:00 - 4:00pm.
Teaching Assistant Renee Mirka
Email: rmirka AT ucsd DOT edu
Office Hours: Tuesday 12-2pm, AP&M 6446
Teaching Assistant Pieter Spaas
Email: pspaas AT ucsd DOT edu
Office Hours: Wednesday 2-4pm in AP&M 5829, Thursday 8:30-10:30am in AP&M 7218
Sections 927126, 927127, 927128
Course content 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.
Resources recommended
in addition
Formal prerequesite Math 18 or Math 20F or Math 31AH, and Math 20C. Students who have not completed listed prerequisites may enroll with consent of instructor.
Credit Hours: 4 units
Homework information Homework will be announced via TritonED on Fridays after lecture. You can submit your homework to the mailboxes on Friday's before 11am in the morning (before the lecture starts). All submissions must be in handwritten form.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://www-senate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship.

Grading Information

The final grade will composed 20% homework and either (a) 20% of the first midterm, and 20% of the second midterm, and 40% of the final exam or (b) 20% of the best midterm and 60% of the final exam, depending on what gives the better result.

Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

A+ A A- B+ B B- C+ C C-
100 - 96.66 96.65 - 93.33 93.32 - 90.00 89.99 - 86.66 86.65 - 83.33 83.32 - 80.00 79.99 - 76.66 76.65 - 73.33 73.32 - 70

The above scale is guaranteed: for example, if your cumulative average is at least 73, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

Course Calendar

Lecture Content
# 1, 1M
08.01.2018.
Administrativa. Examples and Motivation.
# 2, 1W
10.01.2018.
Statements, Implications, Equivalences.
# 3, 1F
12.01.2018.
Propositions and Logical operators: and, or, negation, either-or. Truth tables. Composition of logical operations.
Homework 1 announced.
# 4, 2M
15.01.2018.
Martin Luther King Day
# 5, 2W
17.01.2018.
Further logical connectives. Naive Set Theory
# 6, 2F
19.01.2018.
Classes. Naive Set Theory: set-theoretical operations.
Homework 1 collected. Homework 2 announced.
# 7, 3M
22.01.2018.
Binary Operators in Set Theory. Quantifiers.
# 8, 3W
24.01.2018.
Quantifiers, continued.
# 9, 3F
26.01.2018.
Ordered Pairs and Cartesian Products.
Homework 2 collected. Homework 3 announced.
#10, 4M
29.01.2018.
Some examples for proofs.
#11, 4W
31.01.2018.
First Midterm.
#12, 4F
02.02.2018.
Further examples for proofs. Elementary number theory: well-ordering principle and divisibility.
Homework 3 collected. Homework 4 announced.
02.02.2018: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
#13, 5M
05.02.2018.
Elementary number theory: division-remainder theorem, prime numbers, greatest common divisor.
#14, 5W
07.02.2018.
Euclidean algorithm, Bezout's lemma. Infinitiy of the number of prime numbers.
#15, 5F
09.02.2018.
Fundamental theorem of arithmetics. Applications.
Homework 4 collected. Homework 5 announced.
#16, 6M
12.02.2018.
Fundamental theorem of arithemetics, continued. Infinitude of prime numbers.
#17, 6W
14.02.2018.
Mersenne prime numbers.
#18, 6F
16.02.2018.
Mersenne prime numbers. Two examples for mathematical induction.
Homework 5 collected. Homework 6 announced.
#19, 7M
19.02.2018.
President's Day
#20, 7W
21.02.2018.
Functions
#21, 7F
23.02.2018.
Functions.
Homework 6 collected. Homework 7 announced.
#22, 8M
26.02.2018.
Second Midterm.
#23, 8W
28.02.2018.
Tuples and Sequences. Relations.
#24, 8F
02.03.2018.
Equivalence Relations. Orders.
Homework 7 collected. Homework 8 announced.
#25, 9M
05.03.2018.
Partial Orders on Functions.
#26, 9W
07.03.2018.
Total Orders. Lexicographical ordering on Cartesian Products.
#27, 9F
09.03.2018.
Operations on Equivalence Classes. Modulo Arithmetics
Homework 8 collected. Practice Material for Final Published..
09.03.2018: Deadline to with "W" grade on transcript.
#28,10M
12.03.2018.
Modulo Arithmetics continued.
#29,10W
14.03.2018.
Review
#30,10F
16.03.2018.
Review
FI
19.03.2018.
Final Exam. 11:30pm - 2:30pm. CENTR 212 (Lecture Room!)

Helpful Links

Important academic dates for this academic year

Piazza Website for this course