Math 108
This is the website for the course MAT108 at the Department of Mathematics at UC Davis.
The course will have the textbook The Art of Proof by M. Beck and R. Geoghegan.
The goal of the course is to develop mathematical thinking and the ability to produce clear well-organized mathematical arguments, as indicated by the Department Syllabus.
Lectures: MWF 3:10-4:00 PM Hutchinson 115
Textbook: The Art of Proof by M. Beck and R. Geoghegan. The textbook should be accessible through the UC Davis Equitable Access Program. In addition, there is a version available in the authors' website.
Office Hours: Monday 4:15 -5:15 PM MSB 3240, Friday1:00-2:00 MSB 3106.
TA's office hours: 11:30am-1pm in MSB 2240.
Recitations: WELLMN 3. Thursday 5:10-6:00 B01, 6:10-7:00 B02.
Math 108 Tutoring center:
Important Dates: First Day (April 1st), Midterm Test (May 10), and Final Exam (June 10). Additionally, a portfolio draft (May 17), and the final portfolio (June 12).
Problem Sets: Weekly assignments are due on Fridays at midnight, to be submitted through Gradescope.
Here are some links on how to write mathematics well:
Writing Mathematics Well - Francis Su
Guidelines for good mathematical writing - Francis Su
Advice on mathematical writing - Keith Conrad
See the following rubric for a general scheme of how assignments will be graded.
The following textbook has examples of proofs with mistakes: A Transition to Advanced Mathematics, 8th Edition by Douglas Smith, Maurice Eggen, and Richard St. Andre
Assignments
See the following rubric for a general scheme of how assignments will be graded.
Due Friday 4/5 at midnight on gradescope. Here is a LaTex template if you would like to typeset it.
Attempt due on Sunday 4/7 at midnight on canvas. Peer Review due on Tuesday 4/9 at midnight on canvas. To get full points must submit both, and peer review must contain three points of feedback.
Due Friday 4/12. Here is a LaTex template.
Due Sunday 4/14. Peer review due Tuesday 4/16.
Due Friday 4/19. Here is a template
Due Sunday 4/21. Peer review due Tuesday 4/23.
Due Saturday 4/27. Here is a template
Due Sunday 4/28. Peer review due Tuesday 4/30.
Due Saturday 5/4. Here is a template
Due Sunday 5/5. Peer review due Tuesday 5/7.
Midterm will cover material up until modular arithmetic. The practice problems are provided to help you drill.
Midterm
5/10 in class
Portfolio draft
Due Friday 5/17
Homework 6
Due Friday 5/24
Challenge problem 6
Due Sunday 5/26. Peer review due Tuesday 5/28.
Homework 7
Due Friday 5/31
Challenge problem 7
Due Sunday 6/2. Peer review due Tuesday 5/4. Turn in on 6/6 for a grade on gradescope
Course outline and Lecture notes
(with suggested readings and notes - note that my notes are sketches, can contain errors and will not exactly match lectures)
Lecture 1: April 1st. What is a mathematical statement?
Read "Notes for students."
Lecture 1 notes.
Lecture 2: April 3rd. Axioms of the integers, and the naturals. Chapter 1
Lecture 3: April 5th. Principle of Mathematical Induction. Chapter 2
Lecture 4: April 8th. Principle of Mathematical Induction II. Chapter 2.
Went over induction, corrected two induction proofs with mistakes one of which was the statement that all horses are of the same color. If anyone has lecture notes theyre willing to share let me know.
Lecture 5: April 10th. Well ordering principle and greatest common divisor. Chapter 2.
Notes on the well ordering principle. We also proved in class that 2^{k} is greater than or equal to k! for all k greater than or equal to 4.
Lecture 6: April 12th. Review of Logic. Chapter 3
Lecture notes up to the last page. Introduced proof by contradiction and contrapositive
Lecture 7: April 15th. Finish Chapter 3 Chapter 4: recursion
Finished lecture notes on logic
Finished lecture notes on intro to recursion
Lecture 8: April 17. Chapter 4 recursion: binomial coefficient theorem, linear recursion
Finished the following notes. For more on linear recursion see Appendix E on generating functions (a related concept), or the following notes which use linear algebra and generating functions.
Lecture 9: April 19. Finish chapter 4 and start chapter 5: set theory.
Lecture notes on set theory- proved 1/4 of de morgans laws.
Lecture 10: April 22. Chapter 5
Finished the following notes. set theory axioms written out at the end.
Lecture 11: April 24. Equivalence relations. Section 6.1, 6.2, and 6.3.
Lecture notes on relations. covered up to page middle of page 5
Lecture 12: April 26. Modular arithmetic
Lecture notes on relations. Page 5 to page 9. Equivalence classes, partitions.
Lecture 13: April 29. Applications of modular airthmetic. Fermats little theorem
Lecture notes. Finished.
Lecture 14: Functions. Chapter 5.
Lecture notes. These notes will differ a bit from lecture. We defined functions, the domain of a function, the codomain, the graph of a function, the image of a subset of the domain, the preimage of a subset of the domain, injectivity and surjectivity. We did not define cardinality yet.
Lecture 15: Functions continued
Continued Lecture notes. Covered cardinality, injectivity, surjectivity, pigenhole principle.
Lecture 16: Functions continued
Continued Lecture notes. Covered when are two functions equal, function composition, inverses of relations, inverses of functions.
Lecture 17: Midterm Review.
Lecture 18: Cardinality
Lecture 19: Upper and lower bounds
Lecture 20: The reals
Lecture 21: Rational and Irrational Numbers.
Portfolio
See the following handout for instructions on the portfolio: Portfolio. Here is the rubric I will be using. To turn in the LaTex file save it as a pdf and turn it in through gradescope.
Here is a sample .tex file for the portfolio that you can use : you need to copy paste it into a .tex file or into an overleaf tex file.
You can either download LaTex onto your computer or use overleaf (a cloud sharing Latex editor where you need to create an account).
Here are links to tutorials on using LaTex on overleaf:
If you enjoy proof writing/ mathematics and want to explore mathematics or the process of research here are some links. (If you know of any other programs or clubs that may be of interest to your fellow classmates please let me know)
Summer Undergraduate Research Experiences (REU): An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific research project, where he/she works closely with the faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduate students supported with NSF funds must be citizens or permanent residents of the United States or its possessions. Some REU sites or professors have additional funding available for international students. NSF funded REUs
UC Davis directed reading program: The DRP matches undergraduate (mentees) with math graduate students (mentors) to read on a math topic that is not typically covered in the classes offered by the Math department at Davis. This is a chance for undergraduates to dive deeper into math, have one on one discussions with experts, and explore a fun new topic with their mentors.
Undergraduate clubs at Davis that may be of interest: Math club, Association for Women in Mathematics (AWM) Student Chapter, SACNAS student chapter