Math 2705W — Technical Writing in Mathematics

This page contains generic information for MATH 2705W – Technical Writing in Mathematics. Please contact your instructor for specifics about your own section of 2705W.

Course Description:

Description: An introduction to the communication of mathematics through formal writing.

Prerequisites: Prerequisites: ENGL 1007 or 1010 or 1011 or 2011, and MATH 1132Q or 2141Q; completion of or concurrent enrollment in either MATH 2110Q, 2142Q, 2210Q, or 2410Q; open only to Mathematics majors.

Meets: Wednesdays 10:10 – 11:00 online.

Learning objectives:

  1. Write about mathematics clearly, using correct grammar, in a well-organized manner.
  2. Discuss mathematical ideas and results in a clear and concise manner that is understood by others.
  3. Understand your audience: who is the reader of your mathematical piece?
  4. Explain a proof in a manner that is easily understood by a reader.
  5. Use clear and appropriate examples to explain ideas and illustrate points.
  6. Develop documents and presentations that effectively and correctly communicate mathematical ideas.

Goal:

The primary goal of this course is to communicate and discuss mathematics accurately and effectively. The student will improve in their ability to communicate and write clearly about mathematics. This includes understanding the background of the audience and modifying the narrative to fit the level of mathematical sophistication of the reader. Students will also gain a better understanding of how to structure and write a proof. The students will learn how to use LaTeX in order to typeset papers with mathematical content. LaTeX is the free software that mathematicians use to write mathematics. Using the mathematical constructs in LaTeX can help one to focus on how to arrange content logically and in a mathematically correct fashion.

The Purpose of a “W” Course

In a writing-intensive course (W Course), writing should be integral to the learning goals and subject matter of the course. In the language of the General Education Guidelines at UConn, students should not write simply to be evaluated; they should learn how writing can ground, extend, deepen, and even enable their learning of course material.  In addition to questions concerning strategies for developing ideas, clarity of organization, and effectiveness of expression and discipline specific stylistic norms, the W requirement should lead students to understand the relationship between their own thinking and writing in a way that will help them continue to develop throughout their lives and careers after graduation.

The purpose of a writing course in mathematics is to teach students how to communicate mathematics in a precise, concise, and clear manner. Throughout this course, your instructor will emphasize the best practices in writing mathematics, as it pertains to writing mathematical proofs in particular. The student will learn how to gauge the level of mathematical background of the audience (the reader) and learn how to modify a document to fit the mathematical level of the reader (e.g., how much background is necessary for each type of audience). The student of a W course will write drafts, revise drafts and resubmit. The reason why it is crucial to write a draft is so that the document can be peer-reviewed and critiqued by your instructor, so that a conversation can occur about what background may be necessary, and what level of detail is required when discussing a concept or a mathematical proof. In this course, there will be much emphasis on the structure of mathematical writing (examples, lemmas, theorems, corollaries, remarks, etc), and there will be discussions about the importance and educational power of properly chosen examples and diagrams, graphs, to illustrate a document and to illustrate a mathematical argument that may be otherwise hard to grasp by the reader.

“W” Course Grading and Revision Policy

According to university-wide policies for W courses:

  • an overall passing grade on the writing components of the course (the 15+ page assignments described below) is required to pass the course, and
  • all writing components of the course (the assignments described below) must go through a feedback and revision process.

Accordingly, your portfolio will not be considered complete unless you have made revisions addressing the points raised in the assessment of your initial submission and you will not pass the course without a complete portfolio that achieves a passing standard.

About the Instructors

Visit our current courses departmental website for information about instructors teaching this class.

About the Book and Other Resources

    Although there is no book required for this course, we suggest “Mathematical Writing” by Franco Vivaldi (Springer Undergraduate Mathematics Series, 2014th Edition) as a valuable resource for this class.

    LaTeX: The students can install LaTeX for free in their own machines, or use online sites such as overleaf.com to typeset their papers. Supporting references:

    Books on LaTeX:

    • G. Grätzer, “Math into LaTeX,”
    • M. R. C. van Dongen, “LaTeX and Friends.” 

    A few other useful LaTeX resources:

    General resources on writing mathematics:

    Grading Plan

    Five writing assignments (single-spaced and each at least 2, 2, 3, 4, and 4 pages long, respectively) will be assigned. Each assignment will be submitted, and then re-submitted once comments and feedback or insights by the instructor have been addressed. Each final draft is worth 20% of your grade. All assignments must be typeset using LaTeX. The writing portfolio will consist of the compilation of all the assignments completed throughout the semester.

    Grading rubric (this document will be updated often!)

    Assignment topic Tasks
    1. The basic elements of mathematical writing: lemmas, theorems, proofs, examples, inline and displayed equations, numbering and cross-referencing. How to arrange mathematical ideas using these structures and how to typeset them in LaTeX.

    (2 pages)

    		 In this assignment the student will learn some LaTeX basics, by elaborating on a handwritten text, and transforming it into a properly typeset LaTeX document.
    2. Write a precise statement and proof of the quadratic formula.

    (2 pages)

    		 In this assignment the student will create a LaTeX document that states a proper statement of the quadratic formula, and contains a complete proof of the formula, followed by worked out examples.
    3. Including graphics, diagrams, matrices, arrays, hyper-references, tables, and bibliography in your documents (tikz, Geogebra, etc)

    (3 pages)

    		Write a paper about a theorem or result or theory where graphs and graphics play an important role. Include a discussion that references the graphics as an aid to understand the result. Some possibilities:

     

    * Pythagoras’ theorem (and/or Euclid’s “Elements”).

    * The Four Color theorem.

    * Green’s theorem.

    * Pick’s theorem.

    * Bayes’ theorem.

    * Euler’s polyhedron formula.
    4. History of Mathematics

    (4 pages)      

    		 Write a paper about a famous mathematician, which discusses some of their work, and illustrates their mathematical era. Discuss some of their work in detail. Some possibilities:

     

    * Pierre de Fermat and/or Andrew Wiles (and Fermat’s Last Theorem).

    * Maryam Mirzakhani.

    * Emmy Noether.

    * David Hilbert (and Hilbert’s problems).

    * Sophie Germain.

    * Felix Hausdorff.

    * Leibniz and Newton, and the invention of Calculus.

    * Evariste Galois.
    5. Applied Mathematics    

    (4 pages)

                                       

    		Write a paper about an application of mathematics. Some possibilities:

     

    * Cryptography.

    * Graphics (and computer science in general).

    * Engineering.

    * Political Science (e.g., voting methods).

    * Gerrymandering.

    * Medicine.

    * Biological Sciences.

    Lectures Outline

    Week by week schedule:

    1. The importance of communicating mathematics and, in particular, through formal writing. Why LaTeX in communicating mathematics? Installing, and compiling documents using LaTeX. Writing LaTeX papers in an online site such as Overleaf.com
    2. The basic elements of mathematical writing: lemmas, theorems, proofs, examples, inline and displayed equations, numbering and cross-referencing. How to arrange mathematical ideas using these structures and how to typeset them in LaTeX.
    3. Basics of mathematical logic. Translating symbols and quantifiers to words in writing.
    4. Feedback and discussion on the writing assignments from Week 2.
    5. The different types of proofs (e.g., induction, contradiction), and elements of a proof. The difference between examples, a generic example, evidence, and a proof.
    6. How to communicate the idea of a proof. From a schematic proof, to writing a proof in text/prose form.
    7. Feedback and discussion on the writing assignments from Week 5.
    8. Using formulas and equations as part of a proof, and to illustrate a mathematical paper. The role of examples in a math paper.
    9. Feedback and discussion on the writing assignments from Week 7.
    10. Using graphs, diagrams, and images as part of a proof, and to illustrate a mathematical paper.
    11. Feedback and discussion on the writing assignments from Week 9.
    12. How to write a paper about a theorem, or about the work of a mathematician. How to focus the writing on the mathematical content.
    13. How to write a paper about an application of mathematics to other areas. How to include mathematics and figures that explain the strengths of the model.
    14. Feedback and discussion on the writing assignments from Week 11.

    University Policies

    • Policy Against Discrimination, Harassment and Related Interpersonal Violence—The University is committed to maintaining an environment free of discrimination or discriminatory harassment directed toward any person or group within its community – students, employees, or visitors.  Academic and professional excellence can flourish only when each member of our community is assured an atmosphere of mutual respect.  All members of the University community are responsible for the maintenance of an academic and work environment in which people are free to learn and work without fear of discrimination or discriminatory harassment.  In addition, inappropriate amorous relationships can undermine the University’s mission when those in positions of authority abuse or appear to abuse their authority.  To that end, and in accordance with federal and state law, the University prohibits discrimination and discriminatory harassment, as well as inappropriate amorous relationships, and such behavior will be met with appropriate disciplinary action, up to and including dismissal from the University.  Additionally, to protect the campus community, all non-confidential University employees (including faculty) are required to report sexual assaults, intimate partner violence, and/or stalking involving a student that they witness or are told about to the Office of Institutional Equity (OIE). Please be aware that while the information you provide will remain private, it will not be confidential and will be shared with University officials who can help.An exception to this reporting exists if students disclose information as a part of coursework submitted to an instructor in connection with a course assignment. Even in the absence of such obligation, all Employees are encouraged to contact OIE if they become aware of information that suggests a safety risk to the University community or any member thereof. The University takes all reports with the utmost seriousness.   More information, including resources and reporting options, is available at equity.uconn.edu and titleix.uconn.edu.
    • Student Conduct Code—Students are expected to conduct themselves in accordance with UConn’s Student Conduct Code.
    • Academic Integrity Statement—This course expects all students to act in accordance with the Guidelines for Academic Integrity at the University of Connecticut. Because questions of intellectual property are important to the field of this course, we will discuss academic honesty as a topic and not just a policy.  If you have questions about academic integrity or intellectual property, you should consult with your instructor.  Additionally, consult UConn’s guidelines for academic integrity.
    • Copyright—My lectures, notes, handouts, and displays are protected by state common law and federal copyright law. They are my own original expression and I’ve recorded them prior or during my lecture in order to ensure that I obtain copyright protection. Students are authorized to take notes in my class; however, this authorization extends only to making one set of notes for your own personal use and no other use. I will inform you as to whether you are authorized to record my lectures at the beginning of each semester. If you are so authorized to record my lectures, you may not copy this recording or any other material, provide copies of either to anyone else, or make a commercial use of them without prior permission from me.
    • Students with Disabilities—The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible.  If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860) 486-2020, or http://csd.uconn.edu/.
    • Final Exam Policy—In accordance with UConn policy, students are required to be available for their final exam and/or complete any assessment during the time stated. If you have a conflict with this time you must obtain official permission to schedule a make-up exam with the Dean of Students. If permission is granted, the Dean of Students will notify the instructor. Please note that vacations, previously purchased tickets or reservations, graduations, social events, misreading the assessment schedule, and oversleeping are not viable reasons for rescheduling a final.

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