Graduate Student Orientation 2007

Orientation for entering graduate students will run from Wednesday August 8 through Friday August 24 (with some final homework problems due on Monday August 27). The first meeting will be at 10:00am Wednesday August 8 in room 199 Cupples I. The tentative plan is that on MWF we will study analysis in the 10am-noon session, go to lunch together, then study linear algebra in a 3:00pm-5:00pm session. On TT you will work on exercises in a less structured fashion. The classroom will be available, as well as other places in Cupples I where you can work together with each other or with a mentor.

First social event: Dinner at 6:00 pm Saturday Aug 11 at my house. Details and directions will be given in our Friday Aug 10 afternoon session.

Here is a tentative schedule for what material we'll cover. Adjustments will be made whenever they seem advisable. Two copies of each text book are on one-day reserve in the math library.

Analysis

Text: Introduction to Analysis, by Arthur Mattuck.

The plan is to cover Chapter 21 Improper integrals, Chapter 26 Integrals with a parameter, and Chapter 27 Differentiating Improper Integrals.
In class we'll do the Questions in each section and the Exercises at the end of each chapter. The Problems at the end of the Chapter are homework, to be written up and handed in at the date noted in the schedule below.

Wed, Aug 8, 10am-noon: Introduction and Sect. 21.1 Improper Integrals: Basic Definitions.

Fri, Aug 10, 10am-noon: Sect. 21.2 Comparison Theorems and Sect. 21.3 The gamma function.

Mon, Aug 13, 10am-noon: Sect. 21.4 Absolute and conditional convergence.

Wed, Aug 15, 10am-noon: Problems at the end of Chapter 21 are due.
          Sect. 26.1 Integrals depending on a parameter.

Fri, Aug 17, 10am-noon: Sect. 26.2 Differentiation under the integral sign.

Mon, Aug 20, 10am-noon: Sect. 26.3 Changing the order of integration.

Wed, Aug 22, 10am-noon: Problems at the end of Chapter 26 are due.
          Sect. 27.1 Introduction and Sect. 27.2 Pointwise vs. uniform convergence of integrals.

Fri, Aug 24, 10am-noon: Sect. 27.3 Continuity theorem for improper integrals and
         Sect. 27.4 Integrating and differentiating improper integrals.

Mon, Aug 27, 10am: Problems at end of Chapter 27 are due.

Algebra

Text: Linear Algebra, 2nd ed., by Kenneth Hoffman and Ray Kunze. The plan is to cover Chapter 6.
Do the exercises at the end of each section. Some exercises will be collected.

Wed, Aug 8, 3pm-5pm: Introduction.

Fri, Aug 10, 3pm-5pm: Sect. 6.2 Characteristic values.

Mon, Aug 13, 3pm-5pm: Sect. 6.3 Annihilating polynomials.

Wed, Aug 15, 3pm-5pm: Sect. 6.4 Invariant subspaces.

Fri, Aug 17, 3pm-5pm: Hand in designated exercises from Sections 6.2-6.4.
          Sect. 6.5 Simultaneous triangulation and diagonalization.

Mon, Aug 20, 3pm-5pm: Sect. 6.6 Direct sum decompositions.

Wed, Aug 22, 3pm-5pm: Sect. 6.7 Invariant direct sums.

Fri, Aug 24, 3pm-5pm: Sect. 6.8 The Primary decomposition theorem.

Mon, Aug 27, 3pm: Hand in designated exercises from Sections 6.5-6.8.

Gary Jensen
Last modified: Fri Aug 3 15:51:50 CDT 2007