Office Hours During Finals Week

My office hours during finals week are

Monday, April 30 1:00-2:20pm

Tuesday, May 1 9:00-11:20am

Final Exam Schedule

You can find the final exam schedule at missouriwestern.edu/finals.

Last Week of Classes

This is the last week of classes!  We will be reviewing for the final on Tuesday and Thursday.  I have posted subject reviews and a sample final exam in the folder titled "Final Exam Reviews" on the right side of the screen.  Your final will include questions from Voting Theory, Finance, Probability and Statistics, and Graph Theory. Please look over the reviews and come prepared with questions on Tuesday and Thursday.   I will also be providing you with a formula sheet.  I will upload the formula sheet to this folder later this week.

The WeBWork homework has been reopened for you to go back and redo any problems that you missed over the semester.  You can do this until Friday, April 27.  This is a good way to review for the final and to earn back any homework points you lost earlier in the semester.

Our last topic last Thursday was the Shapley-Shubik power index.  This will not be tested on the Final exam since you have not had sufficient time to ask about it, but will be included as an optional bonus question on the final.  Are there other measures of power in weighted voting systems?  How can the electoral college be considered a weighted voting system?  Do certain states have more "power" than others in the electoral college?  Why or why not?  Do a google search and report on your findings in the comments.

Don't forget that the CAS is offering review sessions Monday-Thursday this week from 4pm-6pm each afternoon.  You do not have to stay for the full 2 hours if it doesn't work with your schedule.  I strongly encourage you to take advantage of this review opportunity.

Voting

This week, we've discussed some fairness criteria and started looking at weighted voting systems.

Recall that the state of Maine voted in November to switch to plurality with elimination (called ranked choice voting) for many of their elections.  Here are some interesting articles about this switch and about plurality vs plurality with elimination

Maine's Ranked Choice Voting: It's not Plurality (has a couple interesting videos)

Top 5 Ways Plurality Voting Fails

Maine Ranked Choice Voting Initiative, Question 5(2016) - Ballotpedia

Portland Press Herald

Podcast Meeting with Supporters on Both sides of Question 5 (scroll down to find this)

The Reasons for Maine to Adopt Ranked Choice Voting are Unconvincing

Yes on '5': No More Lesser of Two Evils in Maine

Maine became the first state in the country . . . to pass ranked choice voting

Can you find any interesting articles about Question 5 on Maine's ballot?  How would you have voted on Question 5?

Voting Theory

We will be finishing off the semester with a discussion of voting theory.  The notes and worksheets for this unit can be found on the right side of the blog.  There will only be paper homework for this last unit.  I will collect the first worksheet in class on Tuesday, April 17.

Exam 3

Your third exam for MAT110(E) is scheduled for Tuesday, April 10.  An exam review is located in the Handouts folder linked on the right side of the blog.  Please print this out and bring it with you to class on Thursday.  You should attempt the problems before coming to class so that we can focus our discussion on the problems that students most struggled with.

I have posted a couple videos below reviewing annuities and amortized loans.

After the exam, we will begin a small unit on Voting Theory.  Thank you to everyone who filled out the mid-semester survey to select our last topic.

Refinancing and Paying Ahead

Last week, we saw two ways to save money in an amortized loan.  The first option was to refinance. This means to transfer the outstanding balance of your loan to a newer loan with a lower interest rate (and perhaps a different term).  To do this, you must find the unpaid balance of your loan.  The formula for this looks just like the formula we use for an amortized loan with P replaced by U and the mt in the exponent replaced with N, where N is the number of payments remaining on the loan:
 \[ U = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-N}}{\frac{r}{m}}\right] \]

The second way to save we looked at was to pay extra towards reducing your principal each month.  We called this "paying ahead".  In this situation, we want to use the formula for the amortized loan to solve for t to determine how soon we would pay off the loan.  You should also be able to determine how much money you save by paying a fixed amount extra each month.
 \[ P = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-mt}}{\frac{r}{m}}\right] \]

There are many calculators online to help answer these questions and more about taking out a loan. Below are links to some calculators that you may find useful when you want to consider taking out a loan in the future.

Bankrate.com

Amortization Schedule Calculator

Mortgage Payoff Calculator

Cost of Living Calculator

Is it Better to Rent or Buy?

We will only be considering fixed rate loans in all of our examples.  But lenders may also offer you an adjustable rate mortgage (ARM).  As the name suggests, with an adjustable rate mortgage, your rate can change, depending on market rates.  These loans can be risky - if rates go up, so does your monthly payment.

Challenge Problem: (Due Tuesday, April 10) Determine what kind of job you want to have after you graduate.  Research salaries for this job in your dream town.  Using a home affordability calculator, determine how expensive a house you could afford based on this salary.  Then, go to zillow.com, and choose a home to purchase (in your budget) in your dream town.  Looking at current interest rates, choose a loan.  Given this loan, calculate the following by hand.  (You may use the online calculator to check your answers, but you must also work out the answers by hand.)
1. Your monthly payments.
2. The amount of interest you would pay by just making the minimal monthly payments.
3. The amount of interest you would pay by paying an extra $100 each month and how soon you would be able to pay off the loan.
4. The amount of interest you would pay by paying an extra $250 each month and how soon you would be able to pay off the loan.
Include the resources you used to determine your future salary, home affordability, loan terms, and the Zillow page for the home you chose.

Mid-Semester Survey

Please fill out the Mid-Semester Survey linked below.  You will be asked to log in with your Missouri Western account so that every student is limited to 1 response; however, your email will not be recorded with your responses.  That is, your responses are anonymous.  Please answer honestly.  Note that you are also asked to vote on the next topic we will cover after finance.

Mid-Semester Survey

Finance

This week, we will begin a new unit on Financial Math. Please make sure you print out the notes and bring them with you to class.  We will start this week with a discussion of interest - simple interest and compound interest.  There will be a lot of formulas in this unit, and you will need to practice with them to get comfortable using them.  I will provide you with the formulas (unlabeled) for the exam, so you need to focus on identifying what formulas apply to what problems.  In addition, it will be very important to remember your calculator for class every day in this unit - you don't want to have to do these calculations by hand! Those of you in lab should have been reviewing logarithms and exponentials in that class recently.  We will be using logarithms to help solve problems in this unit; if you need additional review of logarithms, please see me.  The webpage below is also a good source of review for problems involving logs and exponents.

Exponential and Logarithmic Equations

We will be starting with simple and compound interest on Tuesday.   I recorded a video lecture over simple and compound interest last time I taught this class (linked below).  

Mid-term grades will be submitted on Wednesday.  For those of you looking to improve your grade, remember that this unit doesn't build on the content from the previous two units, so you have a fresh start with Finance.  The homework (both online and the paper homework) is an important component of your grade.  Doing the homework is what prepares you to do well on the exam.  If you haven't been keeping up with the homework, now is a good time to start.  Come see me in office hours if you find you are struggling on the homework.  Finally, remember that you get points for participating with the blog.  Click on some links and comment about what you read.  These are easy points and you shouldn't miss out on getting them!  (In the comments on this post, tell me what you hope to learn in this unit and why.)

Extra Lecture Video

I made a video last semester over the most recent material covered in MAT110(E).  I have linked the video below if you would like to use this to review this material.

Remember that our Probability and Statistics exam will be in class on Thursday, March 8.  An exam review is posted in the Handouts folder linked on the right side of the blog.  You should try the review problems before class on Tuesday and be prepared with questions you have during class. 

Statistics - Normal Distributions

This week, we are moving forward with our discussion of statistics into Normal Distributions.  You will need your calculators and the z-score table from the end of the notes in class with you every day. The Math is Fun website has a nice interactive Standard Normal Distribution and introduction to the Standard Normal Distribution.  I recommend that you play around with this to get a better understanding of what we are discussing in class.

There is a review worksheet over the standard normal distribution in the Handouts folder linked on the right side of the blog.  I have also posted solutions to the Probability and Counting review in this folder. 

The website fivethirtyeight.com uses a lot of data and publishes articles about their findings.  Visit the site and in the comments describe what you found there.  How does it relate to the statistics we discussed in class?

Challenge Problem (Due Tuesday, March 6): The website fivethirtyeight.com deals with a lot of data and publishes articles on their findings.  Visit the page https://data.fivethirtyeight.com and choose a data set and article to look at.  Read the article.  How do they use the data in the data set?  Download the data (you may need to right-click to download) and try computing some statistics with it.  

No Class Thursday February 22 - Please watch video

There will be no class on Thursday, February 22 due to inclement weather.  I have created a video over the first portion of the statistics notes.  Please watch the video below to make up for the missed class today.

No Class Tuesday February 20

Campus is closed Tuesday, February 20 due to inclement weather.  We will not be having class today.  To make up for this missed class, I have posted a review of Counting and Probability in the Handouts folder linked on the right side of the blog.  You should try these problems on your own and let me know if you have any trouble.  I will be using these reviews in my lab sections on Wednesday to review with my lab students.  Lecture students who are not normally in my labs are welcome to attend these labs to review.  The lab times and locations are listed below.

Wednesday, February 21 9:00 am Murphy 113
Wednesday, February 21 10:00 am  Agenstein 328

Statistics

This week we are moving into statistics.  You'll definitely want to make sure you have your calculator in class with you this week and next.  Statistics is the study of data.  We will start by looking at some ways to organize numerical data and compute some basic numerical summaries, then we'll move into Normal distributions and confidence intervals.

The article "Take a statistics and probability class in college" from slate.com argues that everyone should take a course in statistics and probability.  We aren't able to cover everything that would be covered in an entire semester of statistics, but hopefully after this unit is over, you will have a better understanding of what we mean when we talk about the probability of a person getting the flu or when a newscaster says a candidate has a 70% approval rate in the polls.

The website www.fivethirtyeight.com computes all sorts of statistics.  They also have a weekly "riddle" that uses math, logic, or probability in an interesting way.  Choose one "Riddler" question and read the solution.  (Or try to solve it yourself.)  Were you able to understand the solution?  What didn't you understand?  Were you surprised by the answer?  Print out the riddle and its solution from the website and write a paragraph discussing the riddle and the questions above.  You can go directly to the archive of "Riddler" articles at https://fivethirtyeight.com/tag/the-riddler/.

I will be late to my office hours on Tuesday, February 20.  I hope to be there by 10:00am, but I will also be in my office from 2:00-3:00pm.

Probability

This week, we're finishing up counting and moving into probability.   Be careful when deciding what counting technique to use for a problem.  You should first see if you can break the problem into a sequence of tasks for which you can count the number of ways to perform each task.  Then, applying the Fundamental Counting Principle, you multiply the number of ways to do each task to get the total number of ways to do everything together.  When deciding whether to use a permutation or a combination to count, you should ask yourself "Does order matter?".  If the answer is yes, then you should use a permutation P(n, r).  If order doesn't matter, use a combination C(n, r).

Last time I taught this course, I had a student ask about counting cards.  The podcast This American Life has an interesting episode about card counting.  You can listen to it here.  Listen to the podcast and tell me what you learned in the comments.

Now, we're going to apply our counting skills to find probabilities.  On Tuesday, we talked about sample spaces and events.  Remember that the sample space is the list of all possible outcomes of a random experiment.  The probability of an event is the proportion of times that event is expected to occur in a long sequence of repetitions of a random process.  We looked at an app that models this for the probability of flipping heads when you flip one coin.  The Binomial Coin Experiment App allows you to change the number of coins being flipped and calculates the number of faces showing heads on each flip.  Click on the link and play around with the app.  Try flipping 3 coins (change to n=3 and leave p=0.50) and let the app run for 10000 flips.  The table to the right gives the probability of getting 0, 1, 2,  or 3 heads under the "Dist" column and also displays the empirical probabilities under the "Data" column.  Are these numbers close after 10,000 flips?  How did they compute those probabilities?

Counting

We will start the Probability and Statistics unit off on Thursday with a discussion of counting.  Make sure that you print the notes for this unit.  There are a lot of pages in these notes, so you might want to print multiple slides per page.  (The link to the notes is available on the right side of the blog or on the right side of the WebWork.) You'll also want to make sure you bring your calculators to class for this unit.  We'll kick off the Probability and Stats unit with some discussions of methods of counting this week.  Consider the question below. 

Look at the menu of your favorite pizza shop.  How many different types of crusts, sauces, and toppings are there?  How many different three topping pizzas could you make if a pizza consists of a crust, sauce, and three toppings?  What about four topping pizzas?

These are the kinds of questions we will be able to answer after our discussion of counting.

Challenge Problem (Due Thursday, February 15): Print the menu from your favorite pizza shop.  How many different types of crusts, sauces, and toppings are there?  How many different three topping pizzas could you make if a pizza consists of one crust, one sauce, and three toppings?  What about four topping pizzas? Include the pizza menu with your answer.

Graph Theory in Application

We've talked about several applications of graph theory in our first unit this semester, including the Traveling Salesperson Problem, applications to networks, and other applications.  There are many other ways that graph theory can be applied.  The links below all apply graph theory in other areas. Read one of the articles below and write a response to the article.  Tell me which article you chose and give a brief summary of the article, explaining how graph theory was applied.  Finally, tell me what you thought of the way they applied graph theory in the article.  Were you surprised that graph theory applied in this situation?

“Is Graph Theory Key to Understanding Big Data?”

“Network Theory sheds new light on origins of consciousness”  

Explained: Graphs from MIT News

"New approach to vertex connectivity could maximize networks’ bandwidth” 

"How Sudoku Can Help You Solve The Mysteries Of Graph Theory"

“Rebooting the Human Genome” 

"The Six Degrees of Kevin Bacon"

Upcoming Due Dates and Exam 1

You have now been introduced to all of the Graph Theory concepts for this unit.  We will be spending some more time on these concepts this week to make sure you've got everything straight.  There are a lot of new definitions in this unit.  Definitions are important; without understanding the definitions, it's impossible to answer questions about them! You can expect to see some definitions on the exam. 

There are several due dates coming up.  Here's a reminder:

Graph Theory Worksheet 2 - Due in class Tuesday, Jan 30

Graph Theory WebWork 2 - Due Tuesday, Jan 30

Graph Theory Worksheet 3 - Due in class Thursday, Feb 1

Graph Theory WebWork 3 - Due Feb 2

Graph Theory Worksheet 4 - Due in class Tuesday, Feb 6

Graph Theory WebWork 4 - Due Friday, Feb 9 (but I strongly suggest you complete this assignment before the exam!)

Graph Theory Exam 1 - In class on Tuesday, Feb 6.  

An exam review is posted in the Handouts folder linked on the right of the blog.  You should print this out and bring it to class with you on Thursday. 

It's natural to have some anxiety before an exam.  To help make sure you are well-prepared for this exam, you should first work on learning all of the definitions from this unit.  Then, practice with problems to make sure you can apply what you've learned.  You have a wealth of problems with which to practice from the WebWork, worksheets, and from the reviews we will use in class this week.  Identify the problems you marked wrong when you graded your worksheets and make sure you know how to correct the problem now.  It helps to get yourself in the right mindset before an exam.  

Ideas for response: 

• You can find ideas of things to think about the night before an exam here.  Have you ever used any of these to help prepare yourself for an exam?  Do you have other tricks to help get yourself in the right frame of mind before an exam?
• What do you usually do to prepare for an exam? Do you do anything differently to prepare for a math exam versus an exam in a humanities course?
• Carol Dweck studies mindsets.  Students with a growth mindset have an attitude of "I can't do this. . .yet", while students with a fixed mindset have an attitude of "I can't do this. . .ever".  Watch the short video Mindsets: Fixed vs. Growth and report on what you learned.  Do you think you have a fixed mindset or a growth mindset?

Graph Isomorphisms and Making Mistakes

I've received several questions about problems 12 and 13 in the first WebWork graph theory assignment.  These questions give you a graph and ask you to determine which of the three graphs below is the same graph, represented differently.  It then asks you to give the one-to-one correspondence that identifies the two graphs.  This correspondence is called a graph isomorphism.  These problems can be tricky, and require some thought and creativity to find the right correspondence.  However, it's a valuable exercise to struggle with problems sometimes, and it makes finding the right solution all the more sweet!

Imagine if you had to do this same thing, but for a graph with thousands of vertices!  It might be a daunting task to imagine.  Of course, you wouldn't want to have to try to find this isomorphism by hand, but even asking a computer to do this would be difficult.  In fact, recent research has been trying to determine if there is a way to determine if two graphs are isomorphic "quickly".  A computer scientist, Laszlo Babai, from the University of Chicago, announced in November 2015 that he had found an algorithm to determine if two graphs were isomorphic in quasipolynomial time.  But, in January 2017, another mathematician,  Harald Helfgott, posted that he had found an error in the proof.  It can be frustrating for you to find that you've answered a problem incorrectly in MAT110(E); imagine if you had announced to all of your colleagues that you had solved a problem, only to find that your solution was incorrect.  This happens to professional mathematicians too.  (I, too, have submitted a paper to a mathematics journal claiming to have proven something, only to find that there was a subtle error in my reasoning.  I've still been unable to correct my error!)  Even when we get the answer wrong, there is value in the struggle that it takes to work with a problem.  Maybe those skills that you learned to work with this problem will help you with a problem in the future.  Maybe you'll remember how to correct it just a little bit better because you had to struggle to find the right answer.  Don't focus too much on worrying about making mistakes - everyone will make them - instead, make sure you learn from your mistakes and are ready to apply what you learned in the struggle to the next problem.

Don't worry about Babai - he's corrected the problem in his algorithm.

You can read more about graph isomorphisms and Laszlo Babai's algorithm at the American Mathematical Society's blog on math and the blog Computational Complexity.

In the comments, tell me about a time you struggled with a problem.  What did you do to solve the problem? Did the struggle help the next time you had a similar problem?

Week 2 - Hamiltonian Circuits and Paths

This week we will be finishing up with Euler circuits and moving into Hamiltonian Paths and Circuits and weighted graphs.  A weighted graph is just a graph with numbers (weights) on the edges. Our goal will be to use weighted graphs and Hamiltonian circuits to solve the Traveling Salesman Problem.  We will see three algorithms for solving this: The Nearest Neighbor Algorithm, The Side-Sorted (or Best Edge) Algorithm, and the Repetitive Nearest Neighbor Algorithm.  We will also discuss how to solve this using Brute Force.  You will need to memorize each of these algorithms.  

Don't forget to keep up with the homework on WebWork and the associated worksheets.  Once you complete a worksheet, you should take it to the CAS to grade and correct your work.  Make sure that you mark your mistakes and correct it with a different color writing utensil.  I will collect all the graded/corrected worksheets in class on Tuesdays.

Challenge Problem: (Due Tuesday, January 30) The picture below is the floor plan for the Second Level of the Nelson-Atkins Museum in Kansas City.  Doorways are represented by a break in the wall.  Is it possible to start in one room on this floor, travel through every doorway, closing the door behind you, and return to where you started?  Use graph theory to answer this question.  Your solution should include a graph, explain how the graph is related to the floor plan, and explain how you used graph theory to determine if such a path exists.  If the path exists, give it; otherwise explain why it is not possible. (https://www.nelson-atkins.org/museum-map/)

How to Email Your Professor

Every semester, I receive an email that looks something like the following:

hey mrs. mccune.  did i miss anything important in class today?  also, i don't know how to do number 2.

There are several issues with this email.  First, you should address your instructors as Professor or Dr, unless they have asked to be addressed differently.  (I am Dr. McCune.)   Second, if you must miss class, please acknowledge that you are responsible for the material covered in your absence.  I am happy to give a brief recap of what you missed, but please remember to first consult the syllabus and the notes before composing your email.

If you need help with a specific homework problem, please be clear about which problem you need help with.  For example, "I need help with number two on the webwork Graph Theory set 1". You should tell me what you've tried so far and specifically what part of the problem is giving you trouble.  It is often useful to include an attachment with a picture of your work so that I can best point you in the right direction to solve the problem. 

Finally, be sure to sign your email with your name, course number, and section.  It is especially difficult to respond to an email if I don't know who the sender is.

Wikihow has a nice summary of how to email a professor, which you should apply when emailing any of your professors on campus.

How to Email a Professor

Welcome To MAT110(E)!

Welcome to MAT110/MAT110E! You should be enrolled in MAT110 if you have a 22 or higher on the ACT or passed the math placement exam (MPE) with a 70 or higher. Otherwise, you should be enrolled in MAT110E and MAT110E Lab. Keep in mind that if you fail the lab section, you will fail this MAT110E lecture section as well, regardless of your exam and homework scores in MAT110E. Hence, it is imperative that you attend and actively participate in your MAT110E lab section.  In particular, make sure that you complete each week's homework bank in your lab sections!


Our semester will be broken into three major units: Graph Theory, Financial Math, and Probability and Statistics.  We will have a fourth shorter unit over Voting Theory at the end of the semester.  I hope that you will enjoy learning a little bit about each of these topics and how they are used in your everyday life and the world around you. I'm looking forward to a great semester!


We will be kicking off the semester this week with an introduction to graph theory. A graph is a collection of vertices (think dots) and edges (think lines) between the vertices. We can use graphs to study many things in the world around us. For example, a graph can represent streets and intersections from a map (see The Traveling Salesperson Problem), computer networks, social networks, or even be used to study DNA (see A Graph Theoretical Approach to DNA Fragment Assembly). By the end of this week, you should know what a graph is and be able to describe several properties of a graph. 

A little bit about me: I am in my sixth year as an Assistant Professor of mathematics here at Missouri Western State University. Before coming to MWSU, I spent a year as a visiting assistant professor at Ashland University. I received my PhD from the University of Nebraska-Lincoln in 2011. (Go Big Red!) My husband is also a mathematician at William Jewell College. We have a 3.5 year old daughter and a 1.5 year old son who are both a bundle of energy. 

Please ask for help as soon as you are having trouble with this class. You can visit me in my office (Agenstein 135K). Peer tutoring is also available (for free) through the Center for Academic Support.

Challenge Problem #1: (Due at the start of class on Tuesday, January 23) Sketch several examples of graphs. Determine the degree of the vertices in each graph. When you add the degrees of all the vertices, you will always get an even number. Why is that?