# Dr Mark Coleman - teaching

### Units taught

Year Code Title Role
2016/17 MATH20101 Real and Complex Analysis Course Leader
2016/17 MATH20132 Calculus of Several Variables Course Leader
2016/17 MATH30000 Double Project Course Leader
2016/17 MATH41022 Analytic Number Theory Course Leader
2016/17 MATH60000P Dissertation (90cr) Pure Mathematics and Mathematical Logic Course Leader
2016/17 MATH61000 Double Project Course Leader
2016/17 MATH61022 Analytic Number Theory Course Leader
2016/17 MATH61202 Project Semester Two Course Leader

### Teaching

For 2013\2014 I will be teaching the following three courses.

MATH10101, Sets, Numbers and Functions; This course introduces students to the concept of proof, by studying sets, numbers and functions from a rigorous viewpoint. These topics underlie most areas of modern mathematics, and recur regularly in years 2, 3, and 4. The logical content of the material is more sophisticated than that of many A-level courses, and the aim of the lectures is to enhance students' understanding and enjoyment by providing a sequence of interesting short-term goals, and encouraging class participation.

MATH20101 Real and Complex Analysis; The first half of the course describes how the basic ideas of the calculus of real functions of a real variable (continuity, differentiation and integration) can be made precise and how the basic properties can be developed from the definitions. It builds on the treatment of sequences and series in MATH10242. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.

MATH31022 Analytic Number Theory. We start by giving two proofs of the infinitude of primes. The methods are elementary but poor in that they do not tell us the truth of how many primes there are. Stronger tools are introduced, improving the results until we can indicate, at least in outline, a proof of the Prime Number Theorem

### Teaching for 201314

For 2013\2014 I will be teaching the following three courses.

MATH10101, Sets, Numbers and Functions; This course introduces students to the concept of proof, by studying sets, numbers and functions from a rigorous viewpoint. These topics underlie most areas of modern mathematics, and recur regularly in years 2, 3, and 4. The logical content of the material is more sophisticated than that of many A-level courses, and the aim of the lectures is to enhance students' understanding and enjoyment by providing a sequence of interesting short-term goals, and encouraging class participation.

MATH20101 Real and Complex Analysis; The first half of the course describes how the basic ideas of the calculus of real functions of a real variable (continuity, differentiation and integration) can be made precise and how the basic properties can be developed from the definitions. It builds on the treatment of sequences and series in MATH10242. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.

MATH31022 Analytic Number Theory. We start by giving two proofs of the infinitude of primes. The methods are elementary but poor in that they do not tell us the truth of how many primes there are. Stronger tools are introduced, improving the results until we can indicate, at least in outline, a proof of the Prime Number Theorem

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