Browse Course Material
Course info.
- Prof. Yufei Zhao
Departments
- Mathematics
As Taught In
Learning resource types, mathematical problem solving (putnam seminar), assignments.
Each week there is a lecture (usually by a guest lecturer) on a specific topic or technique, accompanied by a homework problem set. In the following class, students present solutions to problems from the homework. In addition, each week the class is assigned a list of “supplementary problems” ranging from all topics, not necessarily related to the lecture.
Each problem set contains a (sometimes long) list of problems. You are encouraged to work on as many as you like, but only hand in your six best solutions, at least four from the topics problem set based on the lecture. For multi-part problems, you may decide what counts as “one solution,” as long as it is reasonable (i.e., not too trivial).
| SES # | TOPICS | ASSIGNMENTS |
|---|---|---|
| 1–2 | Hidden independence and uniformity |
|
| 3–4 | Sums and integrals |
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| 5–6 | Analysis |
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| 7–8 | Recurrences |
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| 9–10 | Inequalities |
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| 11–12 | Probability |
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| 13–14 | Linear algebra |
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| 15–16 | Abstract algebra |
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| 17–18 | Congruences |
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| 19–20 | Combinatorial configurations |
|
| 21–22 | Generating functions |
|
Additional Topics from Previous Editions of the Course
| TOPICS | ASSIGNMENTS |
|---|---|
| The Pigeonhole principle |
|
| Integer part |
|
| Roots of polynomials |
|
| Limit problems |
|
Acknowledgements
Other than those listed below, all problem sets were created by anonymous guest lecturers.
- All supplementary problems, Hidden independence and uniformity problems , Probability problems , and additional topics assignments from previous editions are based on files created by Prof. Richard Stanley in earlier versions of the course.
- Sums and integrals problems courtesy of Even Chen, a guest lecturer in the class.
- Inequalities problems courtesy of Mehtaab Sawhney, a guest lecturer in the class.
- Congruences problems courtesy of Junyao Peng, a guest lecturer in the class.
All files are used with permission.
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Assignment Problems 7 Hungarian Method of Solving an Assignment Problem The steps for obtaining an optimal solution of an assignment problem are as follows: 1. Check whether the given matrix is square. If not, make it square by adding a suitable number of dummy rows (or columns) with 0 cost/time elements. 2.
Solve the problem • Create a truth table with columns for p, q, r, ~r, p ↔q, and ~r ⋁q. • Cross out rows for which the assumptions p ↔q, ~r ⋁q, and r are false. • In the only remaining row, the conclusion, p, is true . Therefore, the argument is valid. SEES the Problem - Logic Assignment. Slide 6. 𝑝𝑝↔𝑞𝑞 ~𝑟𝑟⋁q
It's thinking on purpose! Critical thinking involves mindful communication, problem-solving, and a freedom from bias or. About This Workbook. egocentric tendency. You can apply critical thinking to any kind of subject, problem, or situation you choose. The activity pages in the Critical Thinking Workbook are meant to be shared and explored.
All supplementary problems, Hidden independence and uniformity problems, Probability problems, and additional topics assignments from previous editions are based on files created by Prof. Richard Stanley in earlier versions of the course. Sums and integrals problems courtesy of Even Chen, a guest lecturer in the class.
Problem 4. Job shop needs to assign 4 jobs to 4 workers. The cost of performing a job is a function of the skills of the workers. Table summarizes the cost of the assignments. Worker1 cannot do job3, and worker 3 cannot do job 4. Determine the optimal assignment using the Hungarian method. Job.
ents a Problem Solving assignment that might be given to students early in the semester. It allows students to practice all the aspects of Problem Solving in the AAC&U Problem S. lving rubric, so it is a good assignment to assess a student's Problem Solving skills. It can be adapted in various ways to any discipline, but there is an expectatio.
Real Life Problem-Solving Scenarios Worksheet (Level 2 & 3) Mary is a friend of yours and she is always on her phone. She doesn't look at you when you are talking to her and you don't think that she is listening. It is making you feel that what you have to say isn't important and you are becoming angry with her when she is on her phone.
solving problems. It is also for people who dislike problem solving or who feel intimidated by problems. And it is for people who want to help others solve problems. For example, many parents may find this book useful for helping their children perform better in school. Business lead
stimulate your creative problem solving parts of your brain, but you'll start to see your world with new eyes. 4 Ways Travel Increases Creativity 5. Structured Walking - Go for a walk down a street or path where there are lamp posts or something else at regular intervals. Now count your steps for alternating intervals.
Enhance accuracy of solving linear systems of equations. 4 Bipartite matching. Can solve via reduction to max flow. Flow. During Ford-Fulkerson, all capacities and flows are 0/1. Flow corresponds to edges in a matching M. Residual graph G M simplifies to:! If (x, y) " M, then (x, y) is in GM.! If (x, y) # M, the (y, x) is in GM. Augmenting path ...
look at the steps of the 80/20 rule:1. Identify the problems and make a list - Wr. te down all the problems that you have. Always try to gather feedback from co-workers, customers or ot. er. who can provide useful information.2. Identify the main cause of each problem - Examine each problem from different persp.
Problem-Solving Tips. e.g., increased responsibilities at When a problem arises, identify your needs and articulate them work, up. ming exams), prioritize your time. Focus. on the most to people w. important issues first. houghts and feelings concerning the Time management is a positive way to reduce stress a.
The 4-Step Problem-Solving Process. This document is the third in a series intended to help school and district leaders maximize the effectiveness and fluidity of their multi-tiered system of supports (MTSS) across different learning environments. Specifically, the document is designed to support the use of problem solving to improve outcomes ...
Chapter 17 The Assignment Problem 301 These problems are all examples of problems which may be solved as as-signment problems. In this chapter we will derive an efficient algorithm for solving assignment problems, and then discuss several problems which may be solved using this algorithm. The assignment problem will then be described in terms ...
Problem solving is the process of designing, evaluating and implementing a strategy to answer an open-ended question or achieve a desired goal. ... steps in a problem-based learning assignment; record of think-aloud protocol while solving a problem). The final product of an assignment that required problem resolution is insufficient without ...
de ne a balanced transportation problem develop an initial solution of a transportation problem using the Northwest Corner Rule use the Stepping Stone method to nd an optimal solution of a transportation problem formulate special linear programming problems using the assignment model solve assignment problems with the Hungarian method. 4.2 ...
1. Problem solving is a skill (it can be learned). It is not an innate ability. 2. Problem solving is fundamentally about attitude and effort (the "problem-solving stance"). 3. The problem-solving stance isn't something that you can just "turn on" when you need it for a test, etc. You have to live it - and successful
The Hungarian Method for Solving the Assignment Problem We're ready to state the Hungarian method now that we've seen a couple of examples. Initialize the algorithm: { Subtract the lowest row value from each row. { For each column, subtract the lowest value. Steps 1 and 2 create zeros to start the algorithm o .
Step One: Define the Problem. The first step, identifying the problem, is a broad review of the current situation — a fitting together of information, like pieces of a puzzle. In this first stage, a group identifies and discusses the symptoms and scope of the problem.
ttitude for problem solving.Debates: Participation in debates necessitates thought processes, listening, logically putting up arguments and counterarguments, placing arguments logically and in the proper sequence, being open to diverse bu. rational views and the like. This encourages critical thinking, esse.
Connection Between Transportation and Assignment Problem An assignment problem is a special case of transportation problem in which m = n, all a i and b j are unity and each is limited to either 0 or 1. Hungarian Method for Solving an Assignment Problem 1. Prepare a square n n matrix. If not, make it square by adding suitable number of dummy ...
Step 3. Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number of such lines is used. Step 4. Test for Optimality: (i) If the minimum number of covering lines is n, an optimal assignment of zeros is possible and we are finished.
Examples of assignment problems VUGRAPH 6 o × assignment or bipartite matching ~minimum cost network flow problem … (Lecture 10) ⇒Can use RELAX to solve assignment problem (Lecture 10) ⇒In this particular case, even 𝜖-relax works as well as RELAX even on sequential computers (Lecture 10) bipartite matching 2n nodes MCNF 2n + 2 nodes ...
The Assignment Problem: An Example A company has 4 machines available for assignment to 4 tasks. Any machine can be assigned to any task, and each task requires processing by one machine. The time required to set up each machine for the processing of each task is given in the table below. TIME (Hours) Task 1 Task 2 Task 3 Task 4 Machine 1 13 4 7 6
PROBLEM SOLVING STRATEGIES Course Team Dr. Tola John Odule (Developer/Writer) Prof. Julius Olatunji Okesola (Content Editor) Dr. Francis B. Osang - HOD/Internal Quality Control Expert ... Assignment questions for the units in this course are contained in the assignment file. Learners will be able to complete their assignments