## MAT401 Mathematics Seminar

Kevin J. Carlin Office: Fo 113 M-F 2:30-4:00 | Telephone: 7563 E-mail: kcarlin@assumption.edu |

### Text

Brown and Churchill, *Complex Variables and Applications*, eighth edition, McGraw-Hill, 2009.

### Electronic Devices

Calculators may not be used in this course. A cell phone or other electronic communication device may not be used as a watch, a calculator, or for any other purpose. They must be put away and completely deactivated during class.

### Topics

**Complex numbers**: arithmetic, complex conjugates, modulus, polar form, de Moivre’s formula, complex roots, neighborhoods, open and closed sets.
**Complex functions**: limits and continuity, derivatives, Cauchy-Riemann equations, analytic functions, harmonic functions, exponential and logarithmic functions, general exponents.

**Integrals**: arcs and contours, contour integrals, Cauchy’s theorem, simply and multiply connected domains, Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, the fundamental theorem of algebra.

### Grading

There will be a midterm exam (October 16) and a final exam. Homework will be collected weekly. Your final grade will be based on 500 points:

Presentations | 200 |

Homework | 100 |

Midterm exam | 100 |

Final exam | __100__ |

| 500 |

Exam grades are based on partial credit and will be scaled. Typically, the scale is A^{-} = 75%, B^{-} = 60%, C^{-} = 50%, D^{-} = 35%.

Make-up of any graded work due to serious illness or other emergency is possible only with prior or immediate notice and will be granted at my discretion. Unexcused absence from any exam will result in a failing grade for the course.

### Learning Objectives

- Students should be able to prepare lecture notes by reading and analyzing a topic from a text. Students should be able to deliver effective oral presentations.
- Students should know the definitions and properties of complex numbers and their polar representations. They should be able to use these to find complex roots. They should understand the elementary geometry and topology of the complex plane.
- Students should understand the concepts of limits, continuity, and the derivative of functions of a complex variable. They should know the relationship between the complex derivative and partial derivatives. They should understand the properties of analytic and harmonic functions.
- Students should know the definition of a complex contour integral. They should know the properties of integrals of analytic functions on various contours. They should be able to apply these in a variety of situations.

### Course Description

**MAT 401 Mathematics Seminar**

The topic is determined by the instructor. Emphasis is placed on student oral presentations. Required course for senior mathematics majors.

### Academic Honesty Policy

The college's academic honesty policy will be enforced as described in the *Student Academic Honesty Policy* booklet. The use of a calculator or any electronic communication device is a violation of this policy.

### College ADA Policy

Assumption College provides accommodation to any student with documented disabilities. If you believe that you are entitled to accommodation, please contact the Director of Disability Services (ext. 7500).

*Last modified August 11, 2009*