#
University of Chicago

Mathematics Department

Inquiry-Based Learning (IBL) Scripts

Webpage maintained by: John Boller, Senior Lecturer in Mathematics

### Basic Description

Inquiry-Based Learning is a teaching technique whereby mathematics students
are presented with scripts of definitions, axioms, and theorems, and are
expected to prove the results for themselves. They present the proofs in
class, and their fellow students criticize the proofs under the supervision
of the instructor.

### History at Chicago

Modern IBL methods have been used in the Mathematics Department
since 2004. Starting with one section of Honors Calculus, the department
has since expanded IBL to include courses in Real Analysis, Honors
Calculus, Elementary Number Theory, and Elementary Geometry.

### Honors Calculus I, II, III (Math 16100-16200-16300)

#### Materials

Here is a proposed
Calendar
for the Autumn Quarter.

Here is the
LaTeX Assignment
and the corresponding
Template.tex
file.

Here is the assignment
Fun with Sets in
(.pdf) and
(.tex) formats.

#### Scripts

Script 0: The Natural Numbers and Mathematical Induction in
(.pdf) and
(.tex) formats.

Script 1: Sets, Functions, and Cardinality
(.pdf)
and
(.tex) formats.

Script 2: Introducing the Continuum
(.pdf)
and
(.tex) formats.

Script 3: The Topology of the Continuum in
(.pdf) and
(.tex) formats.

Script 4: Connectedness, Boundedness, and Compactness in
(.pdf) and
(.tex) formats.

Script 5: Continuous Functions in
(.pdf) and
(.tex) formats.

Script 6: The Field Axioms in
(.pdf) and
(.tex) formats.

Script 7: The Rational Numbers in
(.pdf) and
(.tex) formats.

Script 8: The Real Numbers in
(.pdf) and
(.tex) formats.

Script 9: Sequences and Limits in
(.pdf) and
(.tex) formats.

Script 10: Limits and Derivatives of Functions in
(.pdf) and
(.tex) formats.

Script 11: Uniform Continuity and Integration in
(.pdf) and
(.tex) formats.

Script 12: The Fundamental Theorem of Calculus and the Inverse Function Theorem in
(.pdf) and
(.tex) formats.

Script 13: Series in
(.pdf) and
(.tex) formats.