Math 310 – Foundations for Higher Mathematics (Fall 2019)

Section information

  • Class time and location: M-W-F from 1:00PM to 1:50PM in Crow 204
  • Tentative office hours: Mondays 2:00PM to 4:00PM and Thursdays 12:00PM-2:00PM

Subject

An introduction to the rigorous techniques used in more advanced mathematics. Topics include set theoretic methods of proof, counter-examples, basic logic, foundations of mathematics. Use of these methods in areas such as construction of number systems, counting methods, combinatorial arguments and elementary analysis.

Text

A Concise Introduction to Pure Mathematics by Martin Liebeck, fourth edition, CRC Press, 2016.

Course plan

I hope to cover about twenty chapters in the textbook, although it is possible that we will fall a bit short of this goal. The book consists of short chapters that have some degree of independence, so we have flexibility in which chapters to pick. I plan roughly to follow the order of the book, but not too strictly. My goal is to lead you to a state of mathematical maturity sufficient for you to succeed in our upper level classes, rather than to cover specific topics at length. There will be no serious harm done if we do not cover all of the chapters. At the end of each lecture, I will tell you what I plan to cover in the next few lectures. (If I forget, please remind me to do so.) I strongly encourage you to read ahead of time the chapter to be covered in each lecture.

Coursework, exams and grades

There will be two midterm exams during the semester, and a final exam. These will be held as follows:

  • Midterm 1: October 4, Friday, in class. (1:00PM to 1:50PM in Crow 204)

  • Midterm 2: November 8, Friday, in class. (1:00PM to 1:50PM in Crow 204)

  • Final exam: December 18, Wednesday, 1:00PM to 3:00PM; place to be determined.

IMPORTANT: You are expected to take the exams at their scheduled times. If you are away because of a university sporting event of field trip, then you may arrange for your coach or professor to administer the exam. Excused absences may be granted in the case of illness or bereavement, at my discretion. The final exam cannot be changed for reasons of traveling convenience.

Your final grade will be based on your performance on the three exams and on homework assignments. They will count as follows:

  • Cumulative homework grade: 20%

  • Midterm 1: 20%

  • Midterm 2: 20%

  • Final exam: 40%

I hope and expect that cumulative scores will be such that letter grades will be assigned according to the following scale:

  • A (-, plain, +): cumulative score in [90%, 100%]

  • B (-, plain, +): cumulative score in [80%, 90%)

  • C (-, plain, +): cumulative score in [65%, 80%)

  • D: cumulative score in [50%, 65%)

  • F: cumulative score less than 50%.

The cut-offs for the letter grade sign (-, plain, +) will be set at the very end of the course, when all the scores have been computed. Cut-offs will be set so as to make the overall number of -, plain, + roughly equal. (This is not the same as saying that each letter interval will be subdivided into three subintervals of equal length!)

I may change these cut-off scores if I find it necessary and appropriate, although no changes will be made that would result in a tougher scale than the above.

Please note! I will not under any circumstances deviate from the grading scheme chosen at the end of the semester in order to make changes to one person’s letter grade for the benefit (or detriment) of that individual. This is in part to insure fairness, but also due to the fact that the final exam is relatively late in December, leaving me with very little time to compute and submit grades.

Help resources

In addition to office hours, I will try to facilitate the formation of study groups as follows. Those who are interested in joining a study group should send me an email with the times she or he is available. I will then distribute a list of names, email addresses and times available (only) to the students in the list.

You are permitted to get help on homework assignment problems from me, other students, or anyone else. However, you must write your own answers in your own words.

Good writing

This may be the first math course you take in which the writing of mathematics is just as important as knowing the answer to problems. As everything else, writing mathematics well comes from practice (in particular, from the experience of reading math texts and papers), but a few simple recommendations will go a long way. Keep the following in mind when writing your homework assignments:

  • Never submit your first draft! Once you are happy with your solutions, rewrite them in a clean and orderly way. I will ask the grader to take points from messy and difficult to read assignments. You may find this course a good opportunity to practice writing in latex (this is neither required nor will give you extra points). On the other hand, it is better to write your assignments nicely by hand rather than use a writing program that does not render math symbols properly.

  • Write with empathy! Put yourself in the shoes of the reader. Are you writing so much that the main points of a proof get lost in the middle of lots of trivial observations, or are you writing so little that the reader won’t find your explanations too helpful?

Academic integrity

I will follow the University’s academic integrity policy. If you have any concerns or questions about this policy or academic integrity in class, please contact me.

Email

Please include Math 310 in the subject line of any email message that pertains to this course. You will find my email address on my Home page (see the link on the orange bar at the top of this page).

Homework assignments