Math 479 – Fall 2020: Training Workouts

Below are all of the Training Workouts for Math 479 – Fall 2020 to date. For the most recent Training Workout and additional information see the Math 479 Home Page.

Welcome!

Welcome to Math 479, where great mathematicians are born!  I will post intriguing activities, course announcements, and other exciting information here throughout the semester.  Check back frequently. Below are links to some resources we will be using in the course.

Training Workout #1 – Due Thursday, Aug 20, 2020
  • Work the 10 problems In Training Workout #1 in AiM. No calculators or googling are allowed. If there is a math term or problem statement that you don’t understand you can ask about it on Piazza (include the problem statement in your question so everyone else doesn’t have to log in to AiM to see what you are asking about). You can ask questions about the problem statement, but not about the solution… we will open up that discussion after the due date. You will earn points if I mark your Piazza question as a ‘good question’ and also for answering another student’s clarification question, especially if I mark your answer as endorsed. Focus not only on getting the correct answers, but also coming up with the most clever elegant way to obtain those answers. This is Problem Solving after all!
  • Read: both of the Prefaces in the textbook (pg ix-xiii)
Training Workout #2 – Due Tuesday, Aug 25, 2020
  • Work the 10 Problems in Training Workout #2 on AiM. No calculator, googling, or other software is allowed. If there is a math term or problem statement that you don’t understand you can ask about it on Piazza (if necessary, include the problem statement in your question so everyone else doesn’t have to log in to AiM to see what you are asking about). You can ask questions about the problem statement, or mathematics in general, but not about the solution… we will open up that discussion after the due date. You will earn points if I mark your Piazza question as a ‘good question’ and also for answering another student’s clarification question, especially if I mark your answer as endorsed. Focus not only on getting the correct answers, but also coming up with the most clever elegant way to obtain those answers. This is Problem Solving after all!
  • Post at least one thing to Piazza. It can be a clarification question, a question about the solution to a previously due problem in the course, or an answer or improved answer to a fellow student’s question. You can post a lot more than once too, of course, (the more the better) but at minimum everyone should post at least one thing and read everything that is posted. Naturally don’t post duplicate questions. There’s plenty of math to talk about.
  • Read Section 1.1 in the textbook.
Training Workout #3 – Due Thursday, Aug 27, 2020
  • Work the 10 Problems in Training Workout #3 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date. You will earn points if I mark your Piazza question as a ‘good question’ and also for answering another student’s clarification question, especially if I mark your answer as endorsed. Focus not only on getting the correct answers, but also coming up with the most clever elegant way to obtain those answers. This is Problem Solving after all!
  • Read Chapter 1.2 in Zeitz. In particular, read carefully Example 1.2.1. This is a very instructive and enlightening example!
Training Workout #4 – Due Tuesday, Sep 1, 2020
  • Work the 25 Problems in Training Workout #4 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date.
  • Read Chapter 2.1 in Zeitz.
Training Workout #5 – Due Thursday, Sep 3, 2020
  • Work the 10 Problems in Training Workout #5 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date.
  • Read Chapter 2.1 in Zeitz (if you haven’t already).
Training Workout #6 – Due Tuesday, Sep 8, 2020
  • Work the 25 Problems in Training Workout #6 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date.
  • Start Reading Chapter 2.2 in Zeitz.
Training Workout #7 – Due Thursday, Sep 10, 2020
  • Work the 8 Problems in Training Workout #7 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date.
  • Continue reading Chapter 2.2 in Zeitz (if you haven’t finished it already).
Training Workout #8 – Tuesday, Sept 15, 2020
  • USAMTS!

    Start Working on USAMTS Year 32 Round 1! This is it, team! The first actual official math competition of the season!

    • Get the USAMTS Year 32 Round 1 Problems!
    • Read all of the problems carefully now! That will load them into your brain and allow ideas to simmer to the surface.
    • Start working on them now.
    • Write up a brief (one or two paragraphs per problem) initial progress report to hand in on Tuesday in class. For each of the five problems you should give your initial impressions, and discuss which strategies or problem solving mindsets from Zeitz you think might be helpful as a possible initial approach. If you solve any, don’t hand in your solution, just discuss what problem solving strategies, if any, you used.
    • Be patient! Be confident! Don’t give up easily!!

    Rules: This will be a major consideration in determining your grade in this course, similar to a take-home exam (except that you have more than five weeks to work on it!). We will follow the contest rules stated at the USAMTS website. Read them carefully! You can use reference books, online math references (that don’t involve asking another human being), calculators, Maple, spreadsheets, Geogebra, mechanical models, rulers, protractors, etc. to solve these problems. What you cannot do is discuss the problem with anyone either directly or indirectly (including each other). You can not ask me questions about the problems to clarify the problem statement and so on, but you can ask me to explain Playbook facts, general mathematical terminology, theorems, and any questions about LaTeX.

    These five problems will be due on Monday, October 19, 2020 at 10pm Eastern time by placing a pdf of your solutions in your Dropbox folder. Note that you should hand these solutions in to me, not submit them to the USAMTS competition! Undergraduates are not eligible for this contest, only high school students. Do not write more than one solution on a single sheet of paper (a single problem solution can be on multiple sheets of paper). Neatness counts for this training workout. LaTeX solutions are required. You should use the official LaTeX template provided at the bottom of that page at the USAMTS website. I will answer any LaTeX or Overleaf questions you have. I will try to provide you with a LaTeX template for answering Problem number one. Including figures or diagrams from Geogebra or Asymptote to help your exposition is highly encouraged.

    I will grade it according to the rules of the USAMTS contest. In particular, rule #14 says “Each solution will be given a score of 0, 1, 2, 3, 4, or 5. Solutions will be graded both on mathematical correctness and on writing style.” No solutions will be graded before the due date of October 19.

    Game on!! Go Scranton Mathletes!

Training Workout #9 – Due Thursday, Sep 17, 2020
  • Work the Problems in Training Workout #9 on AiM. No calculator, googling, or other software is allowed.

    If there is a math term or problem statement that you don’t understand you can ask about it on Piazza. You can ask questions about the problem statement, or mathematics in general, but not about the solution. We will open up the discussion for solutions after the due date.
  • Finish reading Chapter 2.2 in Zeitz.
Training Workout #10 – Tuesday, Sept 22, 2020
  • Work on USAMTS Round 1. Put a second draft in your Dropbox folder. For this draft:

    • Use the Overleaf Template – it is linked to in piazza and I sent it to you by email.
    • Answer one or more problems – try to answer at least one problem completely. But two would be even better.
  • Stay active on piazza Don’t post anything about USAMTS, but any other math topics are fine. Your piazza activity is a big part of your course grade.
  • Start reading Chapter 2.3 in Zeitz.