Math 45
Note: The information in this section of the Tutor Library comes from former Learning Center tutors for MATH 45.
Check out the tutoring schedule for the list of available tutors for MATH 45.
Keep in mind: There are several professors for Math 45, so some material may look out of place. Below is a course overview for Professor Jeremy Brandl; other professors' course overview are in progress for the time being.
UNIT 1
Need help on Borda Count? Here's a video that goes through step-by-step on how to complete a Borda Count problem. This is the perfect video if you want to follow along as the video is playing or if you want to test yourself and see how well you understand the process of Borda Count. When you come in to see us for tutoring we can challenge your knowledge and give you insight into how the test will look like.
Edited by Rose 2/22/2021
If you are confused about the weighted voting systems or about Chapter 2 power dynamics here's a great website that goes through all of the material very thoroughly. Some of it you'll need to know for your quizzes and test! There are portions that go into extreme detail and you can skim through those if you find them helpful but don't let it confuse you! The steps and examples are condensed into the images though so feel free to check it out!
Edited by Rose 2/22/2021
Are you confused about the Banzhaf Power Index? Do you know how to find a critical player? This short video is a great example on how to complete a problem using this method. Also, if you are confused, this video does a great job on showing how to find a critical player as well. If you would like a second example with Banzhaf Power Index with a larger weighted voting system check this video out:
*For both videos replace P1, P2, etc with A, B, etc.
Edited by Simran 2/5/2018
Having a hard time? Here is the Practice Exam! Get prepared and come in to tutoring with any questions.
Edited by Teresa 2/28/2020
Math 45 Exam 1 Worksheet.docxUNIT 2
Did you come across a problem in Chapter 3 homework that talked about a sandwich? Were you completely confused about how to solve it? Don't worry! We got your back. The video above goes through how to solve a sandwich problem! Now try the homework problem again or come into the Learning Center and ask us questions.
Edited by Rose 2/22/2021
Having trouble figuring out how people would divide a cake or sandwich fairly? Maybe you want to review the Method of Sealed Bids or Fair Division for an upcoming exam. As usual, the people at LibreTexts have your back. Browse through the various sections for a topic you would like to review. They provide detailed examples and worked out solutions with illustrations to help you better understand the concepts. Check out the link below to start exploring.
Edited by William 2/28/2023
Is apportionment not making any sense? Is it hard to conceptualize these problems and their real-world application? This site explains clearly how apportionment impacts our own US government! The link underneath provides the historic background and an in depth look into why these apportionment methods are needed and how they were used. There are also pages addressing the Hamilton and Huntington-Hill methods provided you search for them.
Edited by Callie 3/11/2024
Now that you have apportionment methods down! Let's talk about how sometimes they don't follow their own rules. These are the paradoxes you'll learn about in class. You should be able to name the three major paradoxes. If you still need them explained a bit more watch this video!
Edited by Rose 2/22/2021
UNIT 3
Are you confused about eulerization and semi-eulerization? Here's a link that gives a simple description of the two with a mini lecture. Hopefully you take some notes on what they're saying because they also offer a mini quiz on the lecture.
Edited by Rose 2/22/2021
Is the cheapest link getting too confusing? They constantly look different and you can't seem to keep track? No worries! We have found a couple of videos that show the two most common ways of how this problem will be presented to you.
Edited by Rose 2/22/2021
This video shows how to find the solution to the Cheapest Link Problem without a given chart. Instead this video shows how to organize the given information to reach the solution.
In this video it shows how to solve a Cheapest Link Problem when all the information is given to you in a chart.
Does the Kruskal's Algorithm make sense to you? You can see an example problem being completed with the video below. You can follow along and see if you can solve it first or just take notes to understand why he is doing each step. We recommend only following up until 1:28.
UNIT 4
We know that you don't use decimals and percentages every day. Some of us may have forgotten how to convert them and that's okay! We're here to offer up a fun way to remember. This website provides the steps and each reason why! There's also example questions you can try out for yourself as well.
Edited by Rose 2/22/2021
Do you remember the probability questions in your homework? The coin toss or the dice problems? This is meant to find the likeliness of an outcome. Here's a video that breaks down why this is important and how to do so. Remember to take some notes to reference later on when working on these problems in the future.
Edited by Rose 2/22/2021