MATH 108: INTRODUCTION TO ABSTRACT MATHEMATICS

Winter 2021



FINAL EXAM

This version replaces an earlier one in which some of the bars were missing from the 0's in problem 7.

All course meetings will be held using zoom.
See Canvas for zoom room numbers and passwords.

Lecturer: Eric Babson, babson@math.ucdavis.edu
Lecture: Mondays, Wednesdays and Fridays at 1:10 pm PST in room 7150588313.
These will be recorded and linked below.
Office hours: for half an hour after class an Monday March 15 (Ides) at 1.
These will normally not be recorded.

Teaching Assistant: James Hughes, jmshughes@ucdavis.edu
Section C01: Tuesdays at 4:10 pm PST in room 91082009446.
Section C02: Tuesdays at 5:10 pm PST in room 98823502329.
Office hours: Thursdays at 4pm PST in room 95723706785.

Text: A Transition to Advanced Mathematics Eighth edition by Smith, Eggen and Andre.

Grading: There will be a total of 400 points possible with 250 points from your best 25 assignments (from among homework assignments and quizzes) and 150 points from the midterm and final split either (50 + 100) or (75 + 75) whichever is better. For final grades a score of at least 360 will yield an A, at least 320 a B, at least 280 a C and at least 240 a D.

Honor Code: Please write and sign (or initial if typed) the following on each assignment and exam:
I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/examination.

Participation: For each lecture a few people can be designated to either keep their cameras on or make a guess at any questions I pose. Each role is worth one extra credit point per lecture for a maximum of 5 points during the term. Please email me if you are willing to fulfill one of these roles during some lecture and I will suggest a date.

Homework: Problems are from the text. Please submit via Gradescope with course entry code WYVR73.
You can type your solutions or write them out and send a picture. Please feel free to discuss the problems with others but if the work you turn in is not entirely your own please cite the group with which you worked.

Midterm: The midterm will cover chapters 1 and 2. One sheet (both sides) of handwritten notes will be allowed. It will be conducted via Zoom (see instructions) and you will scan and upload your solutions to Gradescope. Here is a midterm with solutions and a practice one with solutions from 2020.

Final: The final will be cumulative with more emphasis on the material not on the midterm. It will not be proctored and will be available here at noon on Wednesday March 17 and due by noon on Friday March 19. Here is the spring 2020 final, its answers and a list of practice problems and their answers. You may use the course texts, notes and lectures for the final exam. You may not discuss the exam with others or use other outside materials.

Course Outline: The course covers writing mathematical proofs using set theory as the focus as per the department syllabus.
This is a rough outline of when topics will be covered and will be edited as the term progresses.

Lecture Boardwork:Left Board Right Board


DayDateTopicsHomework Due
MondayJan 41.1 Propositions (av)(aud)
TuesdayJan 5Discussion Quiz 1
WednesdayJan 61.2 Conditionals (av)(aud)1.1.1, 1.1.3dhj, 1.1.6, 1.1.7aeg.
FridayJan 81.3 Quantifiers (av)(aud)1.2.7.de, 1.2.10.bd, 1.2.12.d, 1.2.15bd.
MondayJan 111.4 Direct Proofs (av)(aud)1.3.1.fg, 1.3.4(the first 5 of 7 'Other important properties'), 1.3.7, 1.3.10ab.
TuesdayJan 12Discussion Quiz 2
WednesdayJan 131.5 Indirect Proofs (av)(aud)1.4.5.c, 1.4.7.d, 1.4.9.d, 1.4.11.bde.
FridayJan 151.6 Quantifiers in Proofs (av)(aud)1.5.3.f, 1.5.6.e, 1.5.9, 1.5.12.ace.
MondayJan 18MLK DAY: No Lecture
TuesdayJan 19Discussion Quiz 3
WednesdayJan 201.7 Proof Planning (av)(aud)1.6.2.d, 1.6.4.d, 1.6.6.d, 1.6.9.efg.
FridayJan 221.8 Common Divisors (av)(aud)1.5.10, 1.6.4.i, 1.7.5.e, 1.7.11.adg.
MondayJan 251.8 Division Algorithm(av)(aud)1.8.7.ac, 1.8.17.e, 1.8.21.cdf.
TuesdayJan 26Discussion Quiz 4
WednesdayJan 272.1 Set Notation (av)(aud)1.8.6.cd, 1.8.10, 1.8.13, 1.8.21.abg.
FridayJan 292.2 Set Operations (av)(aud)2.1.6.ef, 2.1.11.c, 2.1.12, 2.1.13, 2.1.19.bdf.
MondayFeb 12.3 Families (av)(aud)2.2.1.j, 2.2.2.i, 2.2.9.e, 2.2.10.d, 2.2.11.df, 2.2.20.abc.
TuesdayFeb 2Discussion Quiz 5
WednesdayFeb 32.4 Induction (av)(aud)2.3.4.ab, 2.3.7.b, 2.3.10.b, 2.3.13, 2.3.19.bcd.
FridayFeb 52.5 More Induction (av)(aud)2.4.4.cj, 2.4.5.g, 2.4.6.b, 2.4.12.ace.
MondayFeb 8Review (av)(aud)2.5.1.a, 2.5.3, 2.5.7.b, 2.5.12, 2.5.14.cde.
TuesdayFeb 9Discussion Quiz 6
WednesdayFeb 10Midterm 1.3.10.ijk, 1.8.12, 2.3.9.d, 2.4.5.i.(Feel free to turn in Friday)
FridayFeb 123.1 Relations (av)(aud)
MondayFeb 15PRES DAY: No Lecture
TuesdayFeb 16Discussion Quiz 7
WednesdayFeb 173.2 Equivalence (av)(aud)3.1.7.adg, 3.1.10.abc, 3.1.11.bc, 3.1.12.b, 3.1.17.abc.
FridayFeb 193.3 Partitions (av)(aud)3.2.1.bgi, 3.2.2.g, 3.2.3.g, 3.2.4.a, 3.2.8.bc, 3.2.19.abc.
MondayFeb 223.4 Modular (av)(aud)3.2.6.be, 3.3.7.a, 3.3.10.a, 3.3.11, 3.3.15.abc.
TuesdayFeb 23Discussion Quiz 8
WednesdayFeb 244.1 Functions (av)(aud)3.4.1.hjkl, 3.4.2.hjkl, 3.4.3, 3.4.4, 3.4.5, 3.4.12.abc.
FridayFeb 264.2 More Functions (av)(aud)4.1.1, 4.1.2, 4.1.6.bd, 4.1.18.ab, 4.1.19.cd.
MondayMar 14.3 In/Sur jectivity (av)(aud)4.1.14.d, 4.1.15.d, 4.2.2.de, 4.2.5.b, 4.2.6, 4.2.13, 4.2.19.bce.
TuesdayMar 2Discussion Quiz 9
WednesdayMar 34.4 Bijections (av)(aud)4.3.1.em, 4.3.2.em, 4.3.6, 4.3.9.bf, 4.3.12.b, 4.3.15.cfj.
FridayMar 54.4 More Bijections (av)(aud)4.4.1.g, 4.4.2.ab, 4.4.3.e, 4.4.5.ab, 4.4.6, 4.4.10.abe.
MondayMar 85.1 Cardinality (av)(aud)4.4.1.cf, 4.4.2.cd, 4.4.3.d, 4.4.7.bcd, 4.4.8, 4.4.10.cd.
TuesdayMar 9Discussion Quiz 10
WednesdayMar 105.2, 5.3, 5.4 Infinities (av)(aud)5.1.1, 5.1.4, 5.1.5, 5.1.8.a, 5.1.13, 5.1.22.bd.
FridayMar 12Review (av)(aud)5.2.6.b, 5.2.12.dg, 5.3.14.abc, 5.3.16.e, 5.4.5, 5.4.9.bc.
Final Exam Cumulative