History of Mathematics
An historical survey of the main lines of mathematical development, covering topics like number theory, analysis, and algebra.
Summary
Past student reviews · Michael Kemeny
One student found the second midterm difficult because it comprised 20% of the grade, contained only four questions, and penalized small errors heavily.
What you’ll be able to do
Recall and state the formal definitions of the mathematical objects and their properties used in various mathematical topics throughout history (e.g., content from number theory, analysis, algebra, etc.).
Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property in the context of these topics.
Recall and state the standard theorems from these topics, and recall the arguments for these theorems and the underlying logic of their proofs.
Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).
Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation, and grammar.
Explain mathematical ideas and describe their historical contexts.
Source: UW Guide 1· UW Guide 2
Grade history
↗All recorded terms · compare terms & instructors
Prerequisites
Course mapProfessors
Spring 2027No instructors recorded for this selection.
Historical instructors & teaching patterns
ANDREI CALDARARU is recorded teaching in Spring 2016, Spring 2018. Recorded history may be incomplete and does not establish a future schedule.
MICHAEL KEMENY is recorded teaching in Fall 2024, Fall 2025. Recorded history may be incomplete and does not establish a future schedule.
ROBERT WILSON is recorded teaching in Spring 2008. Recorded history may be incomplete and does not establish a future schedule.
Recorded history may be incomplete and does not establish a future schedule.
Calendar & sections
Spring 2027Schedule loads here as you scroll.
| Section | Mode | Enrolled / capacity | Waitlist |
|---|
Times are Central. Select a meeting for details; export includes recorded dates for the selected sections.
Meeting source records
Student experience
the class
Past student reviews · Andrei Caldararu
The course split grading between 40% homework and a 60% final project, with students reporting that effort on the project correlated with strong outcomes.
Recent recorded grades — Spring 2024: 3.82 GPA, 94.7% A/AB (n=38 letter grades); Fall 2024: 3.45 GPA, 75.0% A/AB (n=20 letter grades); Fall 2025: 3.46 GPA, 64.3% A/AB (n=14 letter grades).
difficulty & workload
Past student reviews · Michael Kemeny
One student found the second midterm difficult because it comprised 20% of the grade, contained only four questions, and penalized small errors heavily.
Past student reviews · Michael Kemeny
A student felt the class focused on proofs rather than history, noting that exams were made harder because previous scores were high.
Topics
- Historical survey of mathematical development.
- Number theory, analysis, and algebra.
- Historical contexts of mathematical ideas.
Skills
- Recall and state formal definitions of mathematical objects and their properties across historical topics.
- Argue whether mathematical objects satisfy specific types or properties using formal definitions.
- Recall standard theorems, their arguments, and the logic of their proofs.
- Prove or disprove mathematical statements using direct, indirect, example-based, and inductive methods.
- Explain mathematical ideas and describe their historical contexts.
Grades
Latest available · Fall 2025— not enough history to project Spring 2027.
Grade distribution · % of letter grades
Grades over time
Through Fall 2025
More grade details Grade mix, volume & source data
Not enough comparable courses for Spring 2027 in UW–Madison.
Sources & history
Catalog & offerings
Descriptions, prerequisites, and recorded course offerings.
Catalog observation history
Observations at scan time; dates do not imply when a catalog change took effect.
Selected offering source records
No offering records for the selected term.
Raw records
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Student reviews
Original comments behind the course and instructor summaries.
Read original reviews
Grade history
Recorded grade distributions by term, section, and instructor.
Explore recorded gradesRecorded 2026-10-14
Model outputs & technical records
LLM outputs across runs
Full model traces
Recorded model configuration, reasoning, and tool conversations.
Model & dataset provenance
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"task_version": "17",
"output_id": "f77a63e061e1b85653bcbd2c756bf4202388453321ace7a615f1be8ecbecabd2",
"requirements_status": "valid",
"dataset_revision": "fc1811fa52e581ea57a35c0cf3343f8740a8ffbf",
"observed_at": "2026-10-14 17:50:09.728220+00:00"
}