A development of the standard techniques of mathematical proof through an examination of logic, set theory, as well as one-to-one, onto, and inverse functions. Additional topics may be chosen from the topology of the real line, the cardinality of sets, basic number theory, and basic group theory.
- ...translate between formal and informal mathematics.
- ...determine the truth of mathematical statements.
- ...formulate and write mathematical proofs.
- ...read and evaluate mathematical proofs.
Writing-enriched learning outcomes:
- ...demonstrate competency in formal and informal writing specific to Mathematics;
- ...integrate appropriate primary and secondary research into their writing by the means customarily used in Mathematics;
- ...incorporate feedback received during an intensive revision process.
Outcomes for an honors designated class:
- ...conduct independent intellectual inquiry.
- ...articulate how their independent intellectual inquiry contributes to the intellectual landscape of the course.
Math Major Learning Outcomes:
- Critically Analyze: students should be able to determine the validity of a mathematical argument and suggest improvements to that argument.
- Communicate Mathematically: students should be able to communicate mathematical ideas precisely and clearly through written, oral, visual, and/or symbolic forms of expression.
- Abstraction: students should appreciate mathematics in its own right and as a tool for abstraction. They should be able to solve problems using the abstract language and tools of mathematics.
- Mechanical and Computational Skills: students should demonstrate mechanical and computational proficiency in problem-solving using mathematical tools and processes.
New material will be introduced in class (either in lectures or worksheets) or in assigned readings of the textbook (yes, you are expected to actually read some of the book). Reading mathematics is usually hard--if it's not, then you might be doing it wrong. How to read mathematics: take your time, think about what has already been covered, recall relevant examples, think about how the new ideas apply to those examples, read any provided examples carefully, re-evaluate your own thinking, then go on to the next sentence and repeat.
As always, "doing math" requires practice and homework sets are how I make sure you practice. Working with other students is encouraged, but submitted work should reflect your understanding. It's okay to have someone explain their solution to you, but you should make sure you understand the solution and express it in your own words. Homework will be collected approximately weekly and late work will not be accepted unless permission is obtained in advance. Every effort will be made to grade and return homework in a timely manner and you are expected to review graded homework carefully; comments and suggestions on specific problems will be an important way for you to learn from your mistakes.
Exams are a way to measure your progress in the class, but they also encourage you to review material and understand it in the context of later topics. The word "review" may be misleading: studies on learning have shown that merely re-reading the book and notes does not help most students learn (specifically, it does not on average lead to better exam scores). On the other hand, research has shown that trying to figure out what kinds of problems are most likely to appear on the exam and then practicing those kinds of problems can be very helpful. At minimum you should identify the central idea of each section and think about how the homework problems reflect that idea. Exam questions will require you to write proofs, so be sure to practice writing proofs.
Please only turn in work that you think is correct. There is no point in telling you that a proof doesn't work if you already know that to be the case. This means that you might turn in an incomplete argument or add a note saying that you know that something is wrong and where you think that might be. Knowing what you really think helps guide the lessons (and will only ever help your scores).
Assignments, deadlines, worksheets, solutions, past exams, and links to resources will all be posted on the schedule. Keep track of this page (and remember that none of the class material will be on Blackboard).
Over the course of the semester you will create a portfolio of mathematical writing. The portfolio will consist of 9 entries: 6 formal mathematical proofs and 3 other less-formal entries. Proofs will come from a list of portfolio problems. Other entries will be based on readings of different versions of mathematical writing.
Proofs for the portfolio must be written using LaTeX, a free, open-source document preparation system that is universally used for serious mathematical writing. There are a couple of ways to work with LaTeX. The easiest is to use Overleaf, a free, browser-based interface. LaTeX Base is another browser-based compiler (with fewer features). You can also download and install LaTeX on your own computer (it's free, but only sometimes easy; instructions). You can also make use of the computers in certain labs. Examples, links to software sources, and templates are posted on the web site.
The class after a portfolio proof is due will be a peer-review day. You will read portfolio proofs and make suggestions for how they could be improved. This may mean correcting spelling or grammar, but the focus should be on the mathematical content. We will (collectively) develop a rubric to use when evaluating proofs. Comments and suggestions will be returned to the authors, who will then revise their proofs before turning in a final draft for grading.
Always strive for clarity and brevity when writing proofs. Start with a clear statement of the problem and, for complex solutions, a brief statement of the main idea or technique of the solution (e.g. ``proof by contradiction''). Avoid introducing superfluous variables and be sure to specify what each variable is when it is introduced (introductions are an important part of mathematical writing). Unless directed to do otherwise, use actual English words (not just math) to make actual English sentences. More suggestions are in section 5.3 of the textbook.
Grades will be based on homework (30%), exams (28%), portfolios (27%), and worksheets/discussions/other in-class activities (15%). There will be 2 exams during the semester (with the lower score worth 7% and the higher score worth 9%) as well as a final exam (worth 12%). No extra credit will be given. Each portfolio proof will be worth 3% of the final grade, expository entries will be worth 2%, and the assembled portfolio will be worth an additional 3%. Final grades will be assigned using the following rough scale (with plus at the top and minus at the bottom of each interval, as appropriate):
Harassment, non-discrimination, and sexual misconduct:
Consistent with its mission, Gonzaga seeks to assure that all community members learn and work in a welcoming and inclusive environment. Title VII, Title IX and Gonzaga's policy prohibit gender-based harassment, discrimination and sexual misconduct. Gonzaga encourages anyone experiencing gender-based harassment, discrimination or sexual misconduct to talk to someone from the Campus and Local Resources list found in the Harassment and Non-Discrimination Policy.
It may be helpful to talk about what happened in order to get the support needed and for Gonzaga to respond appropriately. There are options for support and resolution, namely confidential support resources, and campus reporting and support options available. Gonzaga will respond to all reports of sexual misconduct in order to stop the harassment, discrimination, or misconduct, prevent its recurrence and address its effects. Responses may vary from support service referrals to formal investigations.
As a faculty member, I want get you connected to the resources here on campus specially trained in and experienced in assisting in such complaints, and therefore I will report all incidents of gender-based harassment, discrimination and sexual misconduct to Title IX (in fact, I am required to report such incidents). A representative from that office will reach out to you via phone and/or email to explore options for support, safety measures and reporting. I will provide our Title IX Director with all relevant details, including names and identifying information, of the information reported. For more information about policies and resources or reporting options, please visit the following websites: Equity and Inclusion and Title IX. If you would like to directly make a report of harassment, discrimination or sexual misconduct directly, you may fill out an online Sexual Misconduct Report Form or contact the Title IX Director by phone, email, or in person:
|Stephanie N. Thomas|
|Title IX Director|
|Business Services Building 018|
Notice to students with disabilities and/or medical conditions:
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability/medical condition requiring an accommodation, please call or visit the Disability Access Office (second floor of Foley Center Library, Room 208.)
Gonzaga University presumes that students have sufficient maturity to recognize their responsibility for regular class engagement, and attendance is a general expectation no matter the teaching modality. However, in order to prioritize the health and safety of all community members, Gonzaga's regular in-person attendance policy may be modified (Amended Class Attendance Policy). I will record attendance solely for the purposes of contact tracing. When we do meet in person, you must follow COVID-related protocols as described in the Student Arrival & Return to Gonzaga Guides, and you will in no way be penalized for following these protocols; see Amended Class Attendance Policy. If you become sick or need to miss class for COVID-related reasons, I will work with you to help you catch up. Don't ever come to class if you are feeling sick. Please communicate directly with me regarding any absences, if possible before they occur.
A note on recorded meetings:
Our class sessions may be recorded for the benefit of students who are unable to attend in-person. Only the instructor may cause a class meeting to be recorded for those students. You shall not make audio or video recordings of class meetings without the prior written authorization of the instructor. By remaining registered in this course, you agree to your voice and image being recorded, and you agree to use any recordings of our class meetings ONLY for the educational purposes of this class (or other sections of this class taught by the same instructor). You agree to delete recordings of our class meetings no later than the end of this semester. You do not have permission to use or share recordings (video or audio) of our class meetings beyond the reach of our class for any purpose, including, but not limited to, posting to any digital application or platform, such as social media. You may not duplicate or distribute recordings of class sessions. In short, your instructor and your classmates intend to appear in these videos only for the purposes of carrying out our teaching and learning in this class. Your compliance with the terms of this syllabus regarding use of class session recordings is subject to the Student Code of Conduct; violations will be reviewed according to the provisions in the Administration of Student Code of Conduct.
FERPA and Privacy:
Under FERPA (Family Educational Rights and Privacy Act), your student records are confidential and protected. Under most circumstances your records will not be released without your written and signed consent; exception includes some directory information. Instructors are not allowed to publicly post grades by student name, social security number, GU student identification number, or any other identifiable means, without written consent from students involved. The FERPA policy does not apply to third party online applications that may be used in courses (i.e. WeBWorK and Gradescope) such that it is the student's responsibility to read the privacy documentation at each website.
All members of the Gonzaga community are expected to adhere to principles of honesty and integrity in their academic endeavors, and I will abide strictly by procedures and guidelines of the University's Academic Integrity Policy. Students and faculty are governed by this policy, and I encourage you to familiarize yourself with its scope and procedures. Ignorance of the policy will not serve as a defense against any violations.
Religious Accommodations for Students
In compliance with Washington State law (RCW 28.10.039), it is the policy of Gonzaga University to reasonably accommodate students who, due to the observance of religious holidays, expect to be absent or endure a significant hardship during certain days of their academic course or program. The Policy on Religious Accommodations for Students describes procedures for students requesting a Religious Accommodation and for faculty responding to such a request.
At Gonzaga, we take teaching seriously, and we ask our students to evaluate their courses and instructors so that we can provide the best possible learning experience. In that spirit, we ask students to give us feedback on their classroom experience near the end of the semester. I will ask you to take a few minutes then to carry out course/instructor evaluation outside class. I very much appreciate your participation in this process; it is a vital part of our efforts at Gonzaga to improve continually our teaching, our academic programs, and our entire educational effort.
Links and class resources
- The Book of Proof
- Proof portfolio
- Math 301 Fall 2018
- Math 301 Spring 2015
- Math 301 Fall 2014
- LaTeX Base
In person in Herak 307A unless otherwise specified, or via Zoom by request.
- Monday 9-10 in the Math Learning Center and 2:30-3:30
- Wednesday 2:30-3:30
- Friday 9:30-10:30
- Or by appointment
Last updated 1/10/2022