Math 479 – Fall 2020: Training Workouts

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.

• 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)

• 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.

• 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!

• 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.

• 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).

• 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.

• 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).

• 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!

• 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.

• 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.

• Work the Problems in Training Workout #11 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 2.3 in Zeitz.

• Work on USAMTS Round 1. Put a third draft in your Dropbox folder. For this draft try to answer at least one more problem than you did on your first draft. If you have solved a problem on the first draft but didn’t write it up, go ahead and write it up. Making figures to include in your solutions also counts as progress (and is a form of getting your hands dirty).

• 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. Continue to discuss previous problems we did not go over that you are interested in.
• Finish reading Chapter 2.3 in Zeitz.

• Work the Problems in Training Workout #11 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 2.3 in Zeitz.

• Work on USAMTS Round 1. Put a fourth draft in your Dropbox folder. For this draft try to answer at least one more problem than you did on your first draft, or complete the proof of a write up that you had partial progress on. Stay focused! Tenacity, confidence, and effort will win the day!

• Solve and prove part (c) of the Magical Rock, Paper, Scissors problem that we worked on in class. Write up your proof in Overleaf in a separate document from your USAMTS round. You can share a single Overleaf document with the members of your team so that everyone can contribute. Put the result in Dropbox in your Captain’s folder.

• 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. Continue to discuss previous problems we did not go over that you are interested in.
• Read Chapter 3.1 in Zeitz.

• Work the Problems in Training Workout #15 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 the Problems for the current round of the WMSETS. This is the second assignment similar to our current USAMTS assignment and all of the same rules apply. You should start a new Overleaf project (separate from USAMTS) for submitting your solutions (do NOT submit anything to WMSETS!). They will be due by placing your pdf in Dropbox before Nov 2, 2020.

• Start reading Chapter 3.2 in Zeitz.

• Start working on WMSETS Round 1. It can be found here. This is due before November 2. Make a new Overleaf project using this template. Save your first draft with the problem solving strategies you think might be relevant and your initial impressions for all five problems and put that draft in Dropbox before class on Tuesday. Stay focused! Tenacity, confidence, and effort will win the day!

• Continue working on USAMTS Round 1. This is due one week from Monday. Stay focused! Tenacity, confidence, and effort will win the day!

• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Finish reading Chapter 3.2 in Zeitz.

• Work the Problems in Training Workout #17 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 3.3 in Zeitz.
• Keep working on USAMTS and WMSETS. USAMTS is due this Monday!

• Hand in USAMTS Round 1 on MONDAY by 10 pm EDT. Put the final version of your USAMTS solutions in your Dropbox folder (clearly named so I know which file it is). I will collect all pdfs on Monday night at 10 pm EDT and graded those according to the USAMTS grading rubric. This is it! Show me what you’ve got!

• Continue working on WMSETS Round 1. This is due before November 2. You do not need to hand in a new draft this week so you can focus your time on finalizing USAMTS.

• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Finish reading Chapter 3.3 in Zeitz.

• Work the Problems in Training Workout #18 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 3.4 in Zeitz.
• Keep working on WMSETS.

• USAMTS Round 2!

  Start Working on USAMTS Year 32 Round 2! This is it, team! The take-home portion of the Final Exam!

  • Get the USAMTS Year 32 Round 2 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, you don’t need to 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 the take-home portion of your final exam in the course. 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 Tuesday, November 24, 2020 at 5:15pm 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 LaTeX template I have made for you that has the diagram for Problem 1 drawn in asymptote. I will answer any LaTeX or Overleaf questions you have. 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 November 24.

  Game on!! Go Scranton Mathletes!

• Continue working on your WMSETS Round 1 This is due before November 2, which is one week from Monday.

• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Finish reading Chapter 3.4 in Zeitz.

• Work the Problems in Training Workout #21 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 4.1 in Zeitz.
• Keep working on WMSETS and USAMTS Round 2.

• Hand in WMSETS Round 1 before midnight (EDT) on SUNDAY, November 1, 2020. Put the final version of your WMSETS solutions in your Dropbox folder (clearly named so I know which file it is). I will collect all pdfs on Monday morning at 12:01AM EDT and graded those according to the USAMTS grading rubric. This is it! Show me what you’ve got!

• Continue working on USAMTS Round 2. This is the take-home portion of your Final Exam. You do not need to hand in a new draft this week so you can focus your time on finalizing WMSETS.

• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Finish reading Chapter 4.1 in Zeitz.

• Work the Problems in Training Workout #23 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.
• Keep working on USAMTS Round 2.

• Work on USAMTS Round 2. Write a draft that has for each of the five problems either (a) your unofficial proposed solution or (b) an explanation of what you think the question is asking in your own words. I want to make sure you are correctly interpreting the questions. Put the draft in Dropbox as usual.
• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Start reading Chapter 4.2 in Zeitz.

• Work the Problems in Training Workout #25 on AiM. On this assignment not everyone has the same set of questions, and you can ask your fellow problem solvers for help on your questions on Piazza. That includes not only asking for problem clarification, but also for ideas about how to answer it. The only thing you can’t ask for is the actual answer, but you can ask for and discuss ideas regarding how to determine the answer. No calculator, googling, or other software is allowed, as usual.

• Keep working on USAMTS Round 2.
• Finish reading chapter 4.2 in Zeitz.

• Continue to work on USAMTS Round 2. Write a new draft that has substantial progress on at least one more problem than you have in previous drafts. Put the draft in Dropbox as usual.
• Stay active on piazza. Don’t post anything about USAMTS or WMSETS, but any other math topics are fine. Your piazza activity is a big part of your course grade. Continue to discuss previous problems we did not go over that you are interested in.
• Start reading Chapter 4.3 in Zeitz.

• Final Exam Part I: Hand in your final solutions to USAMTS Round 2. They are due in Dropbox by 5:15 pm on Tuesday, November 24, 2020 (the start of our final exam period).
• Final Exam Part II: Will be held during our final exam period starting at 5:15 pm on Tuesday, November 24, 2020 (in our usual Zoom meeting room). It will cover the Must-Know Facts posted on Piazza. You Must-Know them well enough to quickly answer MATHCOUNTS Countdown-Round-style questions either in your head or using pencil and paper only. No calculators or references allowed. You Must-Know these facts, after all.