Math 307 Spring 2025

Basic course information

Time: MTWF 13:00–13:50 p.m.
Place: 105 Peterson.
Textbooks:

• Robert Exner et al, Elements of Mathematics, Book 1: Introductory Logic. Part 1, Part 2, Part 3
• Ted Sundstrom, Mathematical Reasoning: Writing and Proof, Version 3
• John P. D'Angelo and Douglas B. West, Mathematical Thinking: Problem-Solving and Proofs, 2nd Edition. Should be available on reserve in the library (but isn't yet).

Prerequisites

Math 247, 252, or 262; or instructor's permission.

Description and goals

The goal of this course is for students to learn to read and write simple proofs, and in particular to tell whether a proof is sound. Although there will be some new material that we will use to practice with proofs, unlike most mathematics courses, the main goals are two particular skills—reading and writing proofs—not new material.

Specific “learning outcomes” include:

• Being able to interpret and use basic concepts from mathematical logic, such as Modus Ponens, in the context of proofs.
• Understanding the notions of tautologies, contradictions, soundness, validity, logical arguments, and truth tables.
• Interpreting and using quantifiers (for all, their exist) in arguments.
• Being able to use proof techniques such as proof by contradiction, counterexamples.
• Being able to write proofs by induction and strong induction (or the well-ordering principle).
• Understanding basic axioms for the integers and more general rings and modular arithmetic, and write simple proofs from these axioms.
• Being able to use the formal definitions of convergence, limits, and continuity in simple examples.

Policies

Grading

Scores will be curved before averaging the different components, in case some component is unexpectedly hard, but a combined raw score of 90% will receive at least an A-, a combined raw score of 80% will receive at least a B-, and so on.

Homework

Homework is due at the end of the day on Mondays, except as noted, by upload to Canvas. (Due dates may change.) There will be a homework assignment due during “dead week”. Well-prepared students should expect to spend 8-12 hours per week (2 to 3 hours per hour of class) outside of class on homework and review.

Late homework will be accepted with a 25% linear penalty per day or part of a day. The lowest two homework scores will be dropped to accommodate illnesses and other unforeseen events.

Exams

Exams will be given in class.

All exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). I will provide a summary of terms to be used on the exams. Using any notes other than the ones I hand out with the exam, or using electronic devices or communicating with anyone except me during an exam constitutes cheating.

With limited exceptions, the university now requires that students who miss an exam be treated the same, independent of the reason. That is, students who miss the exam because of being hospitalized for illnesses must be treated the same as students who skip an exam because they decide they want more time to study. So:

• If you have a conflict with a midterm exam and you alert me at least 10 days in advance, you will have the opportunity to take a version the exam a few days early, without penalty. In particular, this is the mechanism for accommodating the exceptions to the UO Attendance and Engagement policy.
• If you miss one midterm exam, I will compute your midterm exam score by taking a weighted average of your score on the other midterm exam and the final (after normalizing using the class means and standard deviations).
• If you miss both midterm exams, you will have the opportunity to take a makeup midterm 2 within two weeks of midterm 2, at a 15% linear penalty. That is, whatever score you get on the makeup exam will be multiplied by 0.85. If you do not take the exam within two weeks, your midterm exam score will be computed as zero.
• If you miss the final exam and are otherwise passing the class, you will receive an incomplete in the class and have the option to take a makeup exam in the first two weeks of the summer quarter or the first two weeks of the fall quarter, with a 5% linear penalty. If you do not take the exam in that time, I will compute your grade as if you received a zero on the final exam.
• If you miss the final exam but were otherwise failing the class, you will not have an opportunity to re-take the exam, and will receive and F in the class.

(I agree that spelling this out as a quasi-legal agreement, instead of treating you fairly on an individual basis, is dehumanizing.)

Students with disabilities

I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.

Other policies

General university policies, previously included on many course syllabi, can be found here.

Homework Assignments

• Homework 1. Due April 7.
• Homework 2. Due April 14.

Schedule

This schedule is tentative, and may change during the quarter.
Key for the textbooks: D: D'Angelo & West. E: Exner et al. S: Sundstrom. Main references in bold. Material marked with a + does not have a good reference in our textbooks; if you miss those classes, be especially careful to get notes.

Handouts

Handouts will be posted here, in case you lost the physical copy.

• First Day Handout.
• Tautology List, April 2 version.
• Tautologies and Deduction Rules, April 4 version.
• Tautologies and Deduction Rules, April 9 version.

General Advice

Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.

Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles, but if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours. You can also try the drop-in help at the Math Library; some tutors will be able to help with this class and some will not.

Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.