### Number Theory (M328K)

This course is considered a "transition" course at UT Austin; it is intended to be a course in which students learn to construct mathematical proofs. In general, this course is taken after Calculus and prior to taking any analysis or algebra courses. In the IBL Number Theory course our goal is not only to give students the opportunity to investigate Number Theory concepts but to become independent thinkers, problem solvers, strong communicators, and better proof writers. Because of its track record, the IBL Number Theory course is required for students preparing to become mathematics teachers in the UTeach Program.

The Number Theory course materials were developed here at UT Austin.
They appear in an MAA textbook by David Marshall, Ted Odell and Michael
Starbird, entitled *Number Theory Through Inquiry*, which was
published in 2007.

### Discrete Math (M325K)

IBL sections of the Discrete Mathematics course have used
Edward B. Burger's book *Extending the Frontiers of Mathematics:
Inquiries into proof and argumentation*. This is a transition to
proof course with goals similar to those of the Number Theory course.
The course content includes topics such as graph theory and induction,
which are particularly amenable to IBL strategies.

### Honors Discrete Math: An Introduction to Abstract Mathematics (M325KH)

This course focuses on graph theory, group theory, Epsilon-Delta calculus, and topology and emphasizes the mathematical commonalities among them. This course introduces students to the philosophy of higher-level abstract mathematics. The IBL method is particularly well suited for this.

Materials for this course are being developed at UT Austin and are available in draft form. To review the draft materials, go to the Instructor Resources page of this web site.

Back to Top### Introduction to Real Analysis (M361K)/ Real Analysis(M365C)

These analysis courses present a rigorous treatment of the real number system, of real sequences, and of limits, continuity, derivatives, and integrals of real-valued functions of one real variable. Analysis together with algebra and topology form the central core of modern mathematics.

The materials used in these courses are being developed here at UT Austin and will soon be available in draft form.

Back to Top### Topology (M367K)

This undergraduate topology course treats cardinality, the definition of a topological space, countability properties, separation properties, covering properties, continuity and homeomorphisms, and connectedness.

Materials for this course are being developed at UT Austin and are available in draft form. To review the draft materials, go to the Instructor Resources page of this web site.

Back to Top### Graduate Topology (M382C)

This course is one of the basic graduate courses that prepare students for their Ph.D. preliminary examinations. It introduces some useful tools in topology including the fundamental group, covering spaces, and simplicial homology. These ideas aid us in describing topological spaces and distinguishing one topological space from another.

Materials for this course are being developed at UT Austin and are available in draft form. To review the draft materials, go to the Instructor Resources page of this web site.

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