General Information
Instructor: Konstantina Christodoulopoulou
Phone Number: 352-294-2350
Email: kchristod@ufl.edu
Office Hours: MW4 (10:40–11:30) and F3 (9:35–10:25), Little Hall 365
Open Door Policy: You are welcome to drop by to discuss any aspect of the course at any time.
Course Description
A chronological study of the evolution of mathematical thought from primitive counting through modern ideas of the 20th century.
Required and Recommended Textbooks
Required
Stillwell, J. (2010). Mathematics and Its History (3rd ed.). Springer.
Available online through the UF Marston Science Library.
We will cover topics from Chapters 1–14, plus additional material as time permits.
Additional Readings (available through UF Libraries or Canvas)
-
Boyer, C. B., & Merzbach, U. C. (2011). A History of Mathematics.
-
MacTutor History of Mathematics Archives: http://www-history.mcs.st-and.ac.uk/history/
-
Anderson, M., Katz, V. J., & Wilson, R. J. (Eds.). (2009). Who Gave You the Epsilon? Mathematical Association of America.
Prerequisites
MHF 3202 with a minimum grade of C.
Materials / Supply Fees
There is no supply fee for this course.
Course Objectives
By the end of this course, students will be able to:
-
Describe and analyze the development of major mathematical concepts—including geometry, number theory, algebra, and analysis—from ancient civilizations through the 20th century.
-
Explain how different cultures and historical periods contributed to mathematical knowledge, and evaluate the ways in which cultural exchange shaped mathematical progress.
-
Identify significant mathematicians, texts, and discoveries and explain their impact on later developments.
-
Interpret historical mathematical arguments and methods used by earlier mathematicians.
-
Evaluate the role and evolution of mathematical proof across civilizations and centuries.
-
Compare historical and modern forms of mathematical reasoning, identifying similarities and differences in method and notation.
-
Communicate historical and mathematical ideas clearly and effectively in written and oral form.
-
Synthesize primary and secondary sources to construct historically grounded explanations of mathematical developments.
-
Produce a well-researched term paper demonstrating historical insight, mathematical understanding, and clear argumentation for both general and expert audiences.
-
Critically evaluate the significance of mathematical “great ideas” or “great theorems” within their historical context.
Course Schedule
The pace may vary depending on class progress.
Problem sets and readings will be assigned regularly.
Handouts and notes will be posted on Canvas.
Abbreviations:
-
Stillwell = Mathematics and Its History
-
MTM = MacTutor History of Mathematics Archives
-
Boyer = A History of Mathematics
-
AKW = Who Gave You the Epsilon?
All readings are available through the UF Library or in Canvas.
Weekly Topics and Readings
| Week | Topics | Readings / Assignments |
|---|---|---|
| 1 | Egyptian Mathematics | MTM: Overview; Boyer: Ch. 2 |
| 2 | Babylonian Mathematics; Pythagorean Theorem; Irrational Numbers | Boyer: Ch. 3; Stillwell: Ch. 1; Problem Set 1 |
| 3 | Greek Mathematics Overview; Plato & Aristotle; Euclid’s Elements; Ruler & Compass Constructions | Stillwell: Ch. 2; Boyer: pp. 40–58, 74–89, Ch. 5; Problem Set 2 |
| 4 | Polygonal, Prime & Perfect Numbers; Euclidean Algorithm; Pell’s Equation | Stillwell: Ch. 3; Problem Set 3 |
| 5 | Infinity in Greek Mathematics; Archimedes; Diophantus | Stillwell: Ch. 4; Problem Set 4 |
| 6 | Mathematics in India and China | Boyer: Chs. 9–10; Stillwell: Ch. 5, 6.1–6.3, 11.1; Term Paper Proposal Due |
| 7 | House of Wisdom; Fibonacci; Mathematical Awakening of Europe | Boyer: pp. 203–211, 214–215, 226–231; Problem Set 5 |
| 8 | Cubics & Quartics in 16th-century Italy; Bombelli & Viete | Stillwell: 6.5–6.8, 14.1–14.4; MTM: Cardano, Tartaglia, Abel, Galois; Midterm Exam |
| 9 | Early 17th-century Mathematics; Calculus | Stillwell: Ch. 9; MTM: Wallis, Fermat, Descartes, Newton, Leibniz, Euler |
| 10 | Spring Break — No Class | — |
| 11 | Infinite Series | Stillwell: 10.1, 10.2, 10.4, 10.8; Draft Version of Term Paper Due |
| 12 | Catch-up / Selected Advanced Topics (e.g., Number Theory Revival, Epsilon Proofs, Quaternions) | Stillwell: Ch. 11; readings from AKW |
| 13 | Advanced Topics (e.g., Dedekind’s Theorem √2×√3=√6) or Presentations | Stillwell: Ch. 20; readings from AKW; Peer Review Due |
| 14 | Class Presentations | — |
| 15 | Class Presentations | Term Paper Due |
Grading Policy
Assignments will be graded and returned within one week whenever possible.
Course Grading
| Assignment Category | Percentage |
|---|---|
| Problem Sets & In-Class Activities | 25% |
| Midterm Exam | 30% |
| Presentation | 10% |
| Term Paper Proposal | 5% |
| Term Paper Draft & Peer Review | 5% |
| Term Paper | 25% |
Grading Scale
| Grade | Range |
|---|---|
| A | 90–100 |
| A- | 87–90 |
| B+ | 84–87 |
| B | 80–84 |
| B- | 77–80 |
| C+ | 74–77 |
| C | 70–74 |
| C- | 67–70 |
| D+ | 64–67 |
| D | 60–64 |
| D- | 56–60 |
| E | 0–56 |
Grades will not be rounded.
No extra assignments may be offered to individual students.
Assignments and Course Policies
Problem Sets and In-Class Activities
Problem and in-class activities and will be assigned regularly and it will consist of advanced reading assignments, warm-up exercises to discuss and/or present in class, and main exercises assigned after we have covered new material. Details will be posted in Canvas.
Midterm Exam
The midterm exam is scheduled for Friday, March 7; the exam will be in-person during our regular class and it will contain a mixture of mathematical exercises and short answer historical questions. The exam cannot be rescheduled unless you meet the University requirements; see https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx. Absolutely no collaboration on the exam is allowed.
All mathematical solutions will be graded using the following scale:
Grading Rubric
| Score | Description |
|---|---|
| 5 | Correct solution and very well written. |
| 4 | Small errors such as incomplete sentences, abbreviating words, imprecise definitions, or overlooking trivial cases. |
| 3 | Contains an outline of a correct solution and several steps toward this solution, but the writing is unclear or there are gaps in the solution. |
| 2 | Some original steps toward a correct solution but with significant mathematical errors. |
| 1 | Attempt made but no original steps toward a correct solution. |
| 0 | No relevant work or no submission. |
Term Paper
You will choose a mathematical topic to research and complete a paper. The paper should be of length 10-12 pages (without cover sheet or references) typeset using LaTeX (12pt). The main requirement is that your paper must involve a “great idea” or a “great theorem” of mathematics, so it should be about mathematics. The other main requirements are that you should be able to provide a well-supported argument justifying this choice of topic in your topic proposal and discuss the mathematics in your paper with some genuine understanding of it. All papers are expected to be well-written, free from grammatical errors, and have excellent mathematical depth and style. More details and a grading rubric will be provided early in the semester.
- You should direct a significant portion of your paper toward a general university audience and articulate clearly which sections are aimed toward experts.
- You will turn in a first draft of your paper for peer review; the draft must be a complete paper that you will revise to create your final paper submission.
Presentations
Towards the end of the semester, you will give a short presentation of your paper to the whole class. Presentations will be 10-15 minutes and will be evaluated on mathematical content, style, clarity, and organization. Students are expected to attend all presentations. Guidelines and a grading rubric will be provided in Canvas.
Attendance and Participation
You are expected to participate in class discussions. Participation during class is crucial, and it constitutes an important avenue for learning. I encourage you to be active in every class session. In-class discussions and/or activities will be assigned throughout the course. These activities are meant to encourage attendance and allow for brief reflection on the week’s material. Class attendance will be recorded at the discretion of the instructor including by checking presence via participation in class activities. Scores will be recorded in Canvas. Make-ups will be granted only for excused absences consistent with university policies in the undergraduate catalog: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx and require appropriate documentation.
Note: I understand that we all have different levels of comfort regarding speaking in class. If you have any issues that prohibit you from participating in class, I encourage you to contact me as early as possible so we can find ways to make participation work for you in this class.
Submitted Work
Work must be neat, organized, and clearly written.
Submissions not meeting these standards may have points deducted or may be returned ungraded.
Using the Web
Do not search for homework solutions online or use notes from previous semesters.
Your goal is to learn how to write proofs—not to locate solutions.
Internet access is not permitted during exams, and copied solutions are easy to detect.
If you need help, ask your instructor or classmates.
Make-Up Policies
UF attendance and make-up policies apply:
https://catalog.ufl.edu/UGRD/academic-regulations/attendance-policies/
Incomplete Grades
A student who has completed a major portion of the course with a passing grade but is unable to complete the final exam or other course requirements due to illness or emergency may be granted an incomplete, indicated by a grade of “I”. This allows the student to complete the course within the first six weeks of the following semester. You must contact me before finals week to sign an incomplete grade contract https://www.advising.ufl.edu/aac-academics/incomplete-grades/ and must provide documentation of the extenuating circumstances preventing you from taking the final exam. The grade of “I” is never used to avoid an undesirable grade, and does not allow a student to redo work already graded or to retake the course. See the official policy at http://www.math.ufl.edu/department/incomplete-grades/.
Help With Technical Difficulties
UF Help Desk
352-392-HELP (4357)
HUB 132
https://helpdesk.ufl.edu
University Policies and Resources
UF syllabus policies and student resources:
https://syllabus.ufl.edu/syllabus-policy/uf-syllabus-policy-links/