Introduction to Mathematical Proofs

Announcements

  • Midterm exam 2 covered sections 3.1-3 and 4.1-4.
  • As I'm grading the induction homework, I'm noticing a lot of people making the same mistake. If you are trying to show the terms of the sequence a_1, a_2, ... satisfy a closed formula given by some function f(n), the predicate is P(n)="a_n=f(n)". Instead I'm seeing lots of people treating the predicate as a stand-in for f(n).
  • I have updated the description of the Math Culture Points assignment to include revised hard deadlines for points. As discussed in class, the wording was confusing. Hopefully the new wording is better. Note: You should have earned 5 points by Wednesday February 22.
  • I have made some modifications to this week's homework template to improve formatting in the following ways:
    • Solutions will be slightly indented and double-spaced for improved readability and ease of grading.
    • Problem statements will automatically be single-spaced (which will save paper).
  • I have uploaded a template specifically for writing up your math culture points assignments.
  • When reviewing the graded homework, you may see parts of the problem statement circled. This means I don't think you either (1) did the thing that was circled or (2) didn't do it consistently or completely.
  • Some comments on doing the homework:
    • I've modified how the double-spacing works in the homework so that only your answers will be double-spaced this time.
    • If you run into problem compiling your LaTeX homework using MikTeX, delete the line % !TEX TS-program = pdflatexmk from the top of the file.
    • Someone kindly suggested a change to the homework template that will save a little paper. I've uploaded new templates to incorporate the suggestion.
    • You should write in complete sentences.
    • Counterexamples should be specific, not generic, i.e., π+(-π) is a counterexample to the claim that the sum of two irrational numbers is always irrational. Using a generic irrational x∈ℝ\ℚ isn't good form.
    • You should proofread the template to avoid making mistakes.
    • You should ALWAYS justify your answer.
    • Please turn on doublespacing in LaTeX (i.e., have the line \doublespacing appear just below \begin{document}).
    • I frequently make use of standard proofreading marks when grading.
  • As discussed in class, class notes are available through BlackBoard in the Course Materials section. Let me know if there are any problems.
  • Homework is due at the beginning of class on the assigned date.

Resources

We'll be using LaTeX throughout this course. My colleague, David Maxwell, has prepared some excellent installation instructions, which I have modified for use in this course. If you are using a Mac, you should download these, and if you are using a PC, you should download these. If you are running a Linux distribution, you are on your own (but probably don't need any help anyway). You may also find this list of LaTeX math symbols helpful.

Homework Formatting Instructions

  • All homework must be submitted using the homework template provided after the second week of class.
  • You must include a complete problem statement with each exercise.
  • You must write in complete sentences, with appropriate grammar, etc..
  • Your language should be appropriately formal, e.g., the use of specialized symbols such as the inverted capital A in place of the words "for all" should generally be avoided. Look to your textbook for a model of when the use of such symbols or abbreviations is appropriate.

Failure to follow these instructions will result in deductions from your grade.

Interpreting Graded Problem Scores

On the individual homework, I want to give you some idea of how to interpret your performance on each graded exercise, separate from the collective score. These scores inform the score I assign to your individual homework, but don't dictate it. Generally, each graded problem will be assessed on a 5 point scale: 5=entirely or nearly correct, 4=nearly correct but solution is poorly presented or contains a notable error, 3=mostly correct but a significant mathematical error, 2=significant progress in the right direction but multiple errors, 1=a genuine attempt at the problem, 0=little or no real attempt at the problem.

Homework Assignments by Due Date

Corrections to assignments due dates will be written in red.