Below are links to the recordings of the Math Bootcamp in August 2022

Session 1: August 9, 2022

Session 2: August 11, 2022

Session 3: August 16, 2022

Session 4: August 18, 2022

Session 5: August 23, 2022

Session 6: August 25, 2022

 These are study groups affiliated to the Math Help Centre. Interested students are matched with 4 to 7 other study mates to form a group. These study groups are created for each course, and each study group is supposed to meet for at least two hours each week.

To each study group, a teaching assistant knowledgeable in that course will be assigned. The teaching assistant for an additional hour each week will meet with the study group to assist, advise and clarify problems students face relating to the course. If a student already has a study group for a course and their group needs assistance, their group can still register and receive the needed assistance. Student's or groups wishing to enroll in this program for a course should sign up using the link below.

Use this link to sign up for a MHC Study Group

• Limits (MATH 1500, 1510, 1520)
  
• Gaussian Elimination (MATH 1300, 1210, 1010)
  
• Elementary Matrices (MATH 1300)
  
• De Moivre's Theorem (MATH 1210)
  
• Definition of Derivative (MATH 1500, 1510, 1520)
  
• Linear Programming (MATH 1010)
  
• Differentiation Rules (MATH 1500, 1510, 1520)
  
• Implicit Differentiation (MATH 1500, 1510, 1520)
  
• Determinants (MATH 1210, 1300)
  
• Eigenvalues and Eigenvectors (MATH 1300, 1210)
  
• Washer and Shell Method (MATH 1700, 1710)
  
• Trigonometric Integrals (MATH 1700, 1710)
  
• Trigonometric Substitutions (MATH 1700, 1710)
  
• Truth Tables (MATH 1240)
  
• MATH1240 Definitions and Theorems (MATH 1240)
  
• Induction (MATH 1210, 1240)
  

• Logic Workshop Solutions
  
• Limits and Continuity Workshop Solutions
  
• Definition of Derivative and Differentiation Rules Workshop Solutions
  
• Related Rates Workshop Solutions
  
• Pigeonhole Principle Workshop Solutions
  
• Rings Workshop Solutions
  
• Graph Theory Workshop Solutions
  
• Washer and Shell Method Workshop Solutions
  
• Curve Sketching Workshop Solutions
  
• Sketching Parametric and Polar Curves Workshop Solutions
  

Here are some additional resources you may find useful:

• ΣMH Factoring Calculator - This factors any expression and shows the step-by-step process.
• Desmos graphing calculator - This is a very useful website for graphing functions. It's fast and easy to use.
• Wolfram|Alpha - Wolfram|Alpha can do just about anything you would want it to do. Calculate a derivative, find roots of a massive polynomial. It doesn't plot functions as nicely as desmos, but it's fantasic for just about everything else - and not just mathematics. Ask it whatever question you like and it can usually find you an answer.
• mathcentre - This website has short teaching worksheets on a variety of topics. For example, this worksheet can be found in the chain rule section of the differentiation tab and has a massive number of practise questions.
• Khan Academy - Khan Academy has good video content for a lot of different subjects.
• Codeacademy - If you want to learn to code, try this website. As a side note, if you're going to teach yourself to code try to come up with some kind of mini-project to work on as you learn. It will give your learning more of a purpose and make it more enjoyable.
• LevelUp - LevelUp is an online course on UMLearn developed by members of the math department as a supplement for anyone wishing to brush up on their pre-calculus math skills. There are tutorial videos, exercises and quizzes to test your understanding of a variety of pre-calculus topics.

• Three dogs, Beethoven, Lassie and Skip, are sitting at corners of an equilateral triangle of side 15m in a park. Simultaneously, Beethoven starts walking towards Lassie, Lassie starts walking towards Skip and Skip starts walking towards Beethoven. If all dogs are walking at the same speed of 1m/s, how long does it take for all dogs to meet?
  
  Answer: 10 seconds
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• There are 63 coins, all identical in appearance, and all identical weight, except one coin that is slightly heavier that the others. Three men wish to identify the heavy coin from the 63 using a peculiar set of pan scales. These pan scales have three pans places symmetrically about a central pivot point. The only function of the scales is that if two pans carry a load of equal weight and the third pan carries a load of different weight, then the movement of the scales indicates whether the different weight is heavier or lighter than the other two weights.
  Each of the three men must perform one weighing of a selection of coins without the other two men witnessing the result of the weighing. Beforehand, the men can plan a strategy, and after the weighings, they can regroup and compare their results. Is there a strategy such that when the men regroup, then can identify the heavy coin?
  
  Answer: The first man takes 48 of the coins and place 16 on each pan. If all pans weigh the same, he concludes the heavy coin is one of the 15 remaning, so he puts the 48 aside, and leaves the 15 for the next man. If one of the pans is heavier than the others, the first man leaves the 16 coins on the heavy pan for the next man and puts the rest aside. The next man takes 12 of either the 15 or 16 coins depending on the result of the first weighing. He places 4 on each scale. If all pans weigh the same, he leaves the three (or 4) remaining coins for the next man to weigh. If one of the pans weighed more, he leaves the coins from that pan for the third man. The third man now has either three or four coins to weigh. If there are three, he places one on each pan and finds the heavy one. If there are four remaining, he places one on each pan. If one of the pans is heavier then the coin on that pan is the heavy one. If they weigh the same, then the one he didn't weigh is the heavy one.
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• A tennis tournament with n players is held. All the players are paired up and play one game. The winner goes through to the next round. If the number of players in any round is odd, then one randomly chosen player gets to skip the round and play in the next round. This system continues until someone wins the tournament. How many games are played in total in the whole tournament?
  
  Answer: There is a one-to-one correspondence between the number of players who lose a game and the number of games played. Since each player loses exactly one game (except the winner), n-1 games are played.
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• Runner A, runner B and runner C all run a 100m race. Runner A finishes 10m ahead of runner B. Runner B finishes 10m ahead of runner C. How far ahead of runner C does runner A finish?
  
  Answer: 19m. If runner A finishes 10m ahead of runner B, then runner B is running 9/10 the speed of runner A. Likewise, if runner B finishes 10m ahead of runner C, then runner C is running 9/10 the speed of runner B. Therefore if runner A is running at x m/s, runner B is running 9x/10 m/s and runner c is running 9/10*(9x/10) = 81x/100m/s. Therefore, runner C is running 81/100 times the speed of runner A. When runner A has finished the race (i.e., he has ran 100m), runner C has ran 81m, so he is 19m behind runner A.
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