First Semester 2012: Convex Functions

Jonathan M. Borwein

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Plan
We shall study the first few chapters of Convex Functions: Constructions, Characterizations and Counterexamples.

I will also direct individuals to material in the later chapters depending on their interests and background. The web site for the text is right here .

Course Goals

To provide a strong background for research in optimization, analysis, functional analysis, and applied mathematics. To improve the students’ ability to solve mathematical problems and to describe their solutions lucidly.

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Place and Time
V205 (CARMA, The University of Newcastle)
Time 12:00-2:00 pm, Thursday (weekly commencing from Week 2).

Assessment
There will be two graded assignments each counting for 25% of the final mark (Weeks 6 and 10 due), and the final assignment worth 50% (Week 14 due). Some problems in the assignments will be research problems which require some creativity. All problems are taken from the text. Students will be expected to produce their full answers in LaTeX, Maple documents, or similar form. The assignments should be emailed to me for privacy. Questions can be discussed by email at any time. The due date is always midnight Friday.

Assignment 1. Select four varied questions from the Exercises in each of Sections 2.1, 2.2, and 2.3.

Assignment2. Select four varied questions from the Exercises in each of Sections 2.4, 3.1, and 3.2.

I will approve your question selection to make sure they are representative of the material and of varying degrees of difficulty.

Schedule
March 8^th: We will discuss Chapter One. (Please read this chapter before then)

March 22^nd and 29^th: We shall begin Chapter Two. (Please look over all of the chapter before the 22^nd)

April 19^nd and 26^th: we shall finish Chapter two and look at Sections 3.1, 3.2. On May 10 we finish Chapter three.

From then on the class will be largely a reading class and you should select the topics you wish to study out of the rest of the book.