This week, we will be finishing up the notes on probability and moving on to statistics. Make sure you are keeping up with the webwork homework. After Tuesday, you should be able to do all of the questions about probability. Statistics is the study of data. We will start by looking at ways to organize numerical data and to compute some basic numerical summaries.
Your first drafts of the group project have been graded. I have commented on the files in your google drive folder. Make sure you can see the comments and let me know if you have any questions.
Challenge Problem: Research the Monty Hall Problem. Describe the problem and how probability can be used to answer the problem.
Tuesday, February 23, 2016
Tuesday, February 16, 2016
Exam 1 Meetings Quiz
For Exam 1 Meetings Quiz, if you scored below a 70 on exam 1, you must meet with me by Tuesday, February 23 to earn full credit on the quiz. Bring Exam 1 with you and we will go over the exam and discuss ideas to help you do better on the next exam.
If you scored 70-100, you have a 10 out of 10 on the quiz. You do not have to meet with me, but are welcome to do so.
If you scored 61-69, you have a 5 out of 10 on the quiz. If you meet with me, you will receive a 10 out of 10.
If you scored 60 or below, you have a 0 out of 10 on the quiz. If you meet with me, you will receive a 10 out of 10 on the quiz.
Please look over my office hours to find a time to come talk to me. You don't have to make an appointment during office hours; it will just be first come, first served. If none of my office hours work for you, please set up an appointment with me to meet. (Generally 2-3pm on TR are also a good time to meet with me, even though those are not office hours.)
If you scored 70-100, you have a 10 out of 10 on the quiz. You do not have to meet with me, but are welcome to do so.
If you scored 61-69, you have a 5 out of 10 on the quiz. If you meet with me, you will receive a 10 out of 10.
If you scored 60 or below, you have a 0 out of 10 on the quiz. If you meet with me, you will receive a 10 out of 10 on the quiz.
Please look over my office hours to find a time to come talk to me. You don't have to make an appointment during office hours; it will just be first come, first served. If none of my office hours work for you, please set up an appointment with me to meet. (Generally 2-3pm on TR are also a good time to meet with me, even though those are not office hours.)
Monday, February 15, 2016
Week 5: Probability and Statistics
Just a friendly reminder about assignments due this week:
Tuesday, February 16 - Graph Theory Group Project Drafts Due
Thursday, February 18 - Graph Theory Blog Post Due
Please don't forget about these due dates. Your group project drafts should be typed and placed in your google drive folders.
Last week, we started discussing some methods of counting. This week, we will continue with methods of counting on Tuesday with a discussion of combinations and permutations. With permutations, the order in which we choose things matters; with combinations, the order won't matter. A mneumonic to help you remember this is "committee - combination"; "president - permutation".
We will then move on to probability. You'll want to pay close attention to the vocabulary and formulas in this section. You should also make sure that you get comfortable with the notation. For example, P(E) is the probability that event E will occur.
Challenge Problem: In the game of Euchre 5 cards are dealt from a deck consisting of the 9, 10, J, Q, K, A of hearts, diamonds, spades, and clubs. The ideal hand would consist of both J's of a given color and the A, K, Q of one of the suits. (So, Jack of hearts, Jack of diamonds, and A, K, Q of diamonds would be one ideal hand, for example.) Find the probability of getting an ideal hand.
Tuesday, February 16 - Graph Theory Group Project Drafts Due
Thursday, February 18 - Graph Theory Blog Post Due
Please don't forget about these due dates. Your group project drafts should be typed and placed in your google drive folders.
Last week, we started discussing some methods of counting. This week, we will continue with methods of counting on Tuesday with a discussion of combinations and permutations. With permutations, the order in which we choose things matters; with combinations, the order won't matter. A mneumonic to help you remember this is "committee - combination"; "president - permutation".
We will then move on to probability. You'll want to pay close attention to the vocabulary and formulas in this section. You should also make sure that you get comfortable with the notation. For example, P(E) is the probability that event E will occur.
Challenge Problem: In the game of Euchre 5 cards are dealt from a deck consisting of the 9, 10, J, Q, K, A of hearts, diamonds, spades, and clubs. The ideal hand would consist of both J's of a given color and the A, K, Q of one of the suits. (So, Jack of hearts, Jack of diamonds, and A, K, Q of diamonds would be one ideal hand, for example.) Find the probability of getting an ideal hand.
Monday, February 8, 2016
Week 4: Graph Theory and Probability and Statistics
Our graph theory exam is in class on Tuesday this week. Please make sure you review your notes, the worksheets on WebWork, and the review sheet handed out in class. Be sure that you arrive on time to class Tuesday to make sure you have all of the available time to complete your exam. You will only need a pencil, eraser, and calculator for the exam.
We will be starting our Probability and Statistics unit on Thursday with a discussion of methods of counting. Be sure to print the Probability and Statistics notes out and bring them to class with you Thursday. You will also want to be sure to bring your calculator to class every day for this unit.
Don't forget to complete the Graph Theory objectives for your group projects. These are due next week. You should post your solutions in your group google drive folder.
Challenge Problem: The combination n choose r is written C(n, r). You can compute combinations using Pascal's Triangle. This triangle has many interesting properties beyond being used for computing combinations. Research Pascal's Triangle and explain how to use it to find C(6, 4). Then describe 2 other interesting properties of Pascal's Triangle.
We will be starting our Probability and Statistics unit on Thursday with a discussion of methods of counting. Be sure to print the Probability and Statistics notes out and bring them to class with you Thursday. You will also want to be sure to bring your calculator to class every day for this unit.
Don't forget to complete the Graph Theory objectives for your group projects. These are due next week. You should post your solutions in your group google drive folder.
Challenge Problem: The combination n choose r is written C(n, r). You can compute combinations using Pascal's Triangle. This triangle has many interesting properties beyond being used for computing combinations. Research Pascal's Triangle and explain how to use it to find C(6, 4). Then describe 2 other interesting properties of Pascal's Triangle.
Graph Theory Blog Prompt - Due Thursday, February 18
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. For this blog post, I would like you to read one of the articles below and write a 2-3 paragraph 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?
Tuesday, February 2, 2016
Graph Theory Exam Review
Below is a link to the review for our Graph Theory Exam. The exam will be in class on Tuesday, February 9, 2016. Please print the review and bring it to class with you on Thursday. You should look over the problems before coming to class and be prepared with questions that you have over the material.
Graph Theory Exam Review
Graph Theory Exam Review
Monday, February 1, 2016
Week 3 - Graph Theory: Trees and Kruskal's Algorithm
This week we will be finishing up the graph theory material with a discussion of trees and spanning trees. A tree is just a connected graph which contains no circuits. We will be concerned with finding subgraphs of graphs which contain all the original vertices and are trees. These are called spanning trees. Kruskal's algorithm gives us a way to find a spanning tree of minimal weight in a weighted graph. This algorithm should feel familiar to you; it is very similar to the Side Sorted Algorithm, except now our goal will be to end up with a spanning tree rather than a Hamiltonian circuit.
Challenge Problem: A connected graph G has 18 vertices. How many edges does a spanning tree of G have? How many vertices does a spanning tree of G have? What can one say about the number of edges G has?
Challenge Problem: A connected graph G has 18 vertices. How many edges does a spanning tree of G have? How many vertices does a spanning tree of G have? What can one say about the number of edges G has?
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