# Math 479 – Fall 2018: Training Workouts

Below are all of the Training Workouts for Math 479 – Fall 2018 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 30, 2018
• Obtain and organize the following required items for the course. Bring the first two to class with you from now on along with your copy of Zeitz.
• Problem Training Notebook – Record all of your work for problems that require it in this notebook.
• Must-Know Notebook – This can be a separate notebook or a section in the Problem Training Notebook.
• Training Log I put a copy of the Training Log spreadsheet in the Dropbox folder that you share with me (if you haven’t already installed and accepted my shared folder invitation, do that now.) It is due once per week on Tuesday before 6:00pm, and it should cover everything you did for the problem solving course from Tuesday thru Monday inclusive of the previous week. See the sample spreadsheet for examples.
• Work the 30 problems from the problem set you were given in class. If you want to try it under the timed conditions that sixth, seventh, and eighth graders have available, give yourself 40 minutes. Then when you are finished, try to answer the ones you didn’t finish in time. Calculators are not allowed on these problems.
Hand in just the answers you obtained on this set of problems on the official Assignment Answer Form from the link below. Label the form “Training Workout #1” and put your name on it. You can keep the questions. Show your work in your Problem Training Notebook.
• Read: both of the Prefaces in the textbook (pg ix-xiii)
Training Workout #2 – Due Tuesday, Sept 4, 2018
• Hand in the second set of thirty problems you were given in class. Note that you should show your work (for problems you don’t solve in your head) in your Training Notebook. Write your answers on the official Answer form below, and hand that in as discussed in class. Be sure to label it “Training Workout #2” in the upper right hand corner.
• Read the MATHCOUNTS allowable forms of answers page. In particular, you don’t want to lose points for a answer that is correct but isn’t in the right form. For example, if the answer is supposed to be a common fraction, it has to be a reduced fraction, not a mixed number, or a decimal, or a non-reduced fraction. Also for questions where it ask you to find, say, the value of $x$, if the answer is three, don’t write $x=3$ for your answer; just write $3$.
• Hand in your Training Log. Save your updated Training Log spreadsheet by saving it in your Dropbox folder before the start of Tuesday’s class. Make sure it is up to date each week at that time.
• Read Section 1.1 in the textbook.
Training Workout #3 – Thursday, Sept 6, 2018
• Hand in the problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. Remember to try to solve the problems elegantly as quickly and cleverly as possible with as little computation, calculators, algebra, paper and pencil as possible.
• 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 – Tuesday, Sept 11, 2018
• USAMTS!

Start Working on USAMTS Year 30 Round 1! This is it, team! The first actual official math competition of the season!

• Get the USAMTS Year 30 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. Record your progress in your logs as you go.
• 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 website. 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. The only thing you cannot do is discuss the problem with anyone either directly or indirectly. 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, etc.

These five problems will be due on Monday, October 15, 2018 at 8pm by placing a pdf of your solutions in your Dropbox folder. Note that Note that unless you are still in high school or middle school, you should hand these solutions in to me, not submit them to the USAMTS competition! 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. Problem number one can be easily typed in LaTeX using a table or matrix. Including figures or diagrams from Geogebra or Asymptote to help your exposition is highly encouraged.

If you are currently in high school, in addition to handing in your solutions to me as stated above, you must also officially register for the USAMTS contest itself at the USAMTS website (do that now), and submit your official solutions to them as an official participant.

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 16.

Game on!! Go Scranton Mathletes!

Training Workout #5 – Thursday, Sept 13, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round One. Be sure to log your efforts in the training log.
• Read the MATHCOUNTS Vocabulary Handout – linked to below. Write down any terms that you don’t know and either look them up or ask me about them at the start of class.
Training Workout #6 – Tuesday, Sept 18, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• USAMTS Round One. Continue working on Round 1 Problems that you haven’t solved. Hand in a draft of your attempted solution to at least one of the problems #2-5 (not #1). It can be either handwritten or typed in LaTeX. Be sure to log your efforts in the training log.
• Read Over Sections 2.1-2.3 In Zeitz. You don’t need to work all of the examples but familiarize yourself with the material.
Training Workout #7 – Thursday, Sept 20, 2018
• Solve as many of the 8 problems in the set I gave you in class as you can. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes and no calculator. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round One. Be sure to log your efforts in the training log.
• Look over Section 3.1 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #8 – Tuesday, Sept 25, 2018
• Solve the Logic Problem from the 2017 Admissions Test that I gave you in class. Prove your answers. You can hand this in on paper either handwritten or typed.
• Finish reading Section 3.1 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #9 – Thursday, Sept 27, 2018
• Solve as many of the 8 problems on the Training Workout 9 pdf that is in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes and no calculator. Be sure to log your efforts in the training log.
• Hand in your first draft of USAMTS Round One. Solve as many problems as you can. Any correct solutions that are not replaced by a future submission will be given bonus points for being submitted early. Write up your solutions in $\LaTeX$ using the formatting template recommended by USAMTS. Place your pdf in your Dropbox folder, labeled “USAMTS Round 1 draft 1- NAME.pdf” where NAME is replaced by your name. If you use Overleaf to do $\LaTeX$ you can start your document by doing the following.
1. Login to Overleaf. If you don’t have an Overleaf account, you can create one for free.
3. Click on the Menu icon in the upper left hand corner of the Overleaf screen.
4. Choose the “Copy Project” to make an editable copy for your solution. Give it the project name “USAMTS Round 1 draft 1 – NAME” where NAME is your name or nickname. Tell it to create the copy. When it does you will be able to edit that project.
If all goes well you should be in business. Save the pdf of your draft in your Dropbox folder.
• Be sure to update your Training Logs. Keep a record of your hours that you put into training. It is a large facter in determining your course grade.
Training Workout #10 – Tuesday, Oct 2, 2018
• Solve the Rock, Paper, Scissors Problem that I gave you in class. Prove your answers. You can hand this in on paper either handwritten or typed.
• Continue working on USAMTS Round 1. – it is due on October 15, which is only two weeks away.
• Start reading Section 3.2 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
• Update your Training Log. – it is due once per week, before class on Tuesday.
Training Workout #11 – Thursday, Oct 4, 2018
• Solve the ten question set that is in your Dropbox folder. You do not have to prove your answers. Hand this in on the official answer sheet linked to below.
• Continue working on USAMTS Round 1. – it is due on October 15, which is less than two weeks away.
• Finish reading Section 3.2 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
Training Workout #12 – Thursday, Oct 11, 2018
• Continue working on USAMTS Round 1. – it is due on October 15.
• Answer the Stair Climbing Olympics Problem – that I gave you in class. Prove your answers. You can hand it in on paper in class, either handwritten or typed.
• Start reading Section 3.3 in Zeitz You don’t have to work through all of his examples, but you certainly should if you have time.
USAMTS Round 1 Due – MONDAY, Oct 15, 2018
• Hand in your solution to 2018 USAMTS Round One. Put a pdf of your latexed solutions in your Dropbox folder before 8pm on Monday, October 15, 2018. I will collect all solutions at that time. High school students should also submit their solutions online officially to USAMTS. College students should only submit them to me. This will count as your first exam, so partial results will be given partial credit. Game on!
• Finish reading Section 3.3 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #14 – Thursday, Oct, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Start reading Section 3.4 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #15 – Tuesday, Oct 23, 2018
• USAMTS Round 2!

Start Working on USAMTS Year 30 Round 2! This is it, team! The next actual official math competition of the season!

• Get the USAMTS Year 30 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. Record your progress in your logs as you go.
• 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 website. 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. The only thing you cannot do is discuss the problem with anyone either directly or indirectly. 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, etc.

These five problems will be due on Monday, November 26, 2018 at 8pm by placing a pdf of your solutions in your Dropbox folder. Note that unless you are still in high school or middle school, you should hand these solutions in to me, not submit them to the USAMTS competition! 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. Problem number one can be easily typed in LaTeX using a table or matrix. Including figures or diagrams from Geogebra or Asymptote to help your exposition is highly encouraged.

If you are currently in high school, in addition to handing in your solutions to me as stated above, you must also officially submit your official solutions to USAMTS as an official participant.

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 26.

Game on!! Go Scranton Mathletes!

• Try to solve one or two problems from the set I gave you in class – That is practice for the upcoming VTRMC contest we will be taking next Saturday. If you want to get use to exam timing, give yourself 2.5 hours and see how many problems you can answer correctly in that time.
Training Workout #16 – Thursday, Oct 25, 2018
• Solve the 8 problem set in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
Training Workout #17 – Saturday, Oct 27, 2018
• VTRMC!!! Participate in the 2018 VTRMC Competition, this Saturday, October 27, 2018 in room LSC 233 from 9:30am-noon. Show up between 9:00-9:15am to register and get settled. We will go to lunch afterwards. This counts as an exam in the course. Get plenty of rest the night before and hydrate before the contest itself. Game on!
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
Training Workout #18 – Thursday, Nov 1, 2018
• Solve the 8 problem set in your Dropbox folder. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Finish reading Section 3.4 and read over Section 4.1 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #19 – Tuesday, November 6, 2018
• Solve the problem for Training Workout 19 that is in your Dropbox folder. Write up your proof (handwritten is ok, but LaTeX is c)
• Hand in a first draft of USAMTS Round Two. Solve as many problems as you can, but you don’t have to hand in something for every problem on this draft. Write up your solutions in $\LaTeX$ using the formatting template recommended by USAMTS. Place your pdf in your Dropbox folder, labeled “USAMTS Round 2 draft 1- NAME.pdf” where NAME is replaced by your name. If you use Overleaf to do $\LaTeX$ you can start your document by doing the following.
1. Login to Overleaf. If you don’t have an Overleaf account, you can create one for free.
3. Click on the Menu icon in the upper left hand corner of the Overleaf screen.
4. Choose the “Copy Project” to make an editable copy for your solution. Give it the project name “USAMTS Round 2 draft 1 – NAME” where NAME is your name or nickname. Tell it to create the copy. When it does you will be able to edit that project.
If all goes well you should be in business. Save the pdf of your draft in your Dropbox folder.
• Be sure to update your Training Logs. Keep a record of your hours that you put into training. It is a large facter in determining your course grade.
Training Workout #20 – Thursday, Nov 8, 2018
• Solve the 8 problem set I gave you in class. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below.  If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Finish reading Section 4.1 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #21 – Tuesday, Nov 13, 2018
• Answer the 2015 Admissions Test problem I gave you in class. Write up your solution by hand or LaTeX and hand it in on paper in class on Tuesday. Be sure to log your efforts in the training log.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Start reading Section 4.2 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
Training Workout #22 – Tuesday, Nov 20, 2018
• Update your Training Logs! Some of them are getting behind and out of date. These are an important component of your course grade (it’s either this or your Putnam score.)
• Solve the Mathical Card Game problem that is in your Dropbox folder. As usual, you should prove all of your answers. You can write or type your solutions and hand them in in class on Tuesday.
• Solve the 8 problem set I gave you in class on Tuesday. As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 40 minutes. Do not use a calculator or computer.
• Continue working on USAMTS Round Two. Be sure to log your efforts in the training log.
• Start reading Section 4.3 in Zeitz. As usual you don’t have to work through all of the problems but if you have time, you should. It’s great stuff!
USAMTS Round 2 Due – MONDAY,November 26, 2018
• Hand in your solution to 2018 USAMTS Round Two. Put a pdf of your latexed solutions in your Dropbox folder before 8pm on Monday, November 26, 2018. I will collect all solutions at that time. High school students should also submit their solutions online officially to USAMTS. College students should only submit them to me. This will count as your third exam, so partial results will be given partial credit. Game on!
• Finish reading Section 4.3 in Zeitz. You don’t have to work through all of his examples, but you certainly should if you have time. It’s great stuff!
Training Workout #24 – Thursday, Nov 29, 2018
• Solve the eight problems in the Training Workout 24 pdf in your Dropbox folder As usual, you may keep the problems and should hand in your answers on the official Answer Form linked to below. If you want to take it under contest conditions, give youself 10 minutes per pair of questions. Do not use a calculator or computer for anything.
• Update your Training Logs! Some of them are getting behind and out of date. These are an important component of your course grade (it’s either this or your Putnam score.)
PUTNAM! – Saturday, Dec 1, 2018
• Take the 2018 Putnam contest from 10:00am-6:00pm, Saturday, Dec 1, in the LSC 233. Just bring pencils, pens, and erasers. Get sleep the night before. Hydrate. Don’t eat anything strange for breakfast. Study your Must-Know facts. Study your problem solving strategies and plan a mental checklist for using them if you get stuck. Be sure to log your efforts in the training log. Lunch is on the math department at a local restaurant. This counts as Part I of your Final Exam. Game on!
Training Workout #26 – Thursday, Dec 1, 2018
• Hand in your Must-Know Notebook – Get your Must-Know Notebook organized and up to speed and bring that to class to hand in to be graded. Neatness counts. See the syllabus below for details.
• Hand in your Problem Training Notebook – Get your Problem Training Notebook organized and up to speed and bring that to class to hand in to be graded. Neatness does not count. See the syllabus below for details.
• Solve and hand in at least one problem from USAMTS Round 3. – USAMTS Round 3 is now available. I also made an Overleaf template for you to type your solutions. You can hand in any problem, including problem #1, but you don’t have to hand in problem #1 if, say, you hand in problem #2 instead.

Since this is an active contest I cannot tell you if your solutions are correct or not. But if you hand in more than one solution, each solution that has significant progress can be used to make up for a class you missed during the semester when computing your final grade.

Final Exam Part 2 – Thursday, Dec 13, 2018
• Study for Part 2 of your Final Exam. – It will be held in our usual classroom on Thursday, December 13, 2018 at 5:15 pm. Know your Must-know facts inside and out.
• Finish updating your Training Log Spreadsheets. – The will be graded as part of your course grade.  Make sure they are up to date by the time of the Final Exam.