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How To Write Mathematics

Writing Mathematics is a key part of the introductory precalculus and calculus courses at the University of Michigan (Math 105/115/116). The objective of this website is to prepare students to organize and present mathematics in the rigorous manner expected of them in these courses.

What is Team Homework

Along with individual homework, a key feature of these introductory courses are "team homework" assignments. Each team problem requires considerable thought and a complete, well-written solution. Your team earns grades as a whole, so everyone in a team is responsible for each other's learning of the material.

What is HARD about Team Homework

Each final submitted solution is expected to be written in the style of rigorous mathematics. In this style of presentation, the quality of explanation and interpretation is at least as important as the numerical answers. Writing solutions in this manner is often difficult for students unfamiliar with this style of presentation. Unfortunately, most incoming college students have a mathematical background where correct numerical answers were the sole criteria for quality.

How this Website Can Help You

The objective of this website is to help you adapt your writing skills to mathematics. There is no formula for good mathematical writing just as there is no formula for writing a good paper. This is a skill you develop with time. However, there are several characteristics of good mathematics writing that should always be addressed. This website attempts to break down and explain four such characteristics.

Four Characteristics of Good Mathematical Writing

This website focuses on the following four characteristics of good mathematical writing. Each solution should:

  1. Begin with a restatement of the question

  2. You Restate The Problem by explaining what the problem is asking for as you understand it.

  3. Include computations with explanations

  4. Computations With Explanations are mathematical expressions which are continually being justified and clarified by prose.

  5. Provide figures, graphs, tables, etc. whenever appropriate

  6. End with a clear, concise conclusion.

  7. Conclusions are the results of your computations as well as insightful observations about these results.

For a careful discussion of each characteristic, see the links on the sidebar. Each characteristic is explained in video tutorials in which numerous examples are discussed. Following each video are additional examples to test your understanding.  

Technical Requirements

The video tutorials require running a browser with the latest version of flash player.