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Professor David Groisser
About this courseThis is a first course in complex analysis, which means the calculus of functions of a complex variable. We learn that complex-differentiability has astounding consequences that real-differentiability does not. This leads to a beautiful and rich theory with many applications.
This is not a first course in complex numbers, which is a precalculus topic. You are expected to have experience and facility with complex numbers, their arithmetic, and how they arise in the solving of quadratic equations. You are expected to be familiar with Euler's formula, ei θ = cos(θ) +i sin(θ), from either precalculus or your differential equations course.
While some theorems and proofs will be presented in the course, they will be presented as a means for the student to understand the material, rather than for the sake of rigor. Students will not be expected to exhibit the proof-writing skills that are needed for courses having MAS 4105 (Linear Algebra) as a prerequisite. However, students may be required to do elementary proofs, such as establishing that a formula is correct.
Prerequisites for this courseGrade of C or better in MAC 2313 (or MAC 3474) and in MAP 2302. But just having met the prerequisites on paper does not mean you are prepared for this course; you need to have retained what you learned (or were supposed to learn). This is a problem for many students, especially those whose last calculus class was a year or more ago, or who put fewer hours per week into their past college-level math classes than what college teachers and advisors (not fellow students) recommend—at least two hours per week of out-of-class study for every hour in class—rather than the minimum with which they were able to get by. You will need to have the tools from calculus and precalculus, including trigonometry, at your fingertips, in order for us to make a dent in the syllabus for a first course in complex analysis. There simply is not time in the semester to review even a fraction of what you need to have retained from your previous math classes, from middle school up through Calculus 3. Each student must take upon him/herself the responsibility to do whatever review he/she needs, before that background material is used in our class. This may mean making up for a lot of hours that you did not put into previous math classes.
Why does this course have two numbers and names?MAA 4402/5404 is one of UF's many "piggy-back" courses, in which some students are registered under an undergraduate number, and some under the graduate number. This arrangement is common at UF for courses that are appropriate for both advanced undergraduates and graduate students; it would not be cost-effective to run two nearly identical courses, segregated by graduate/undergraduate status. Since many graduate students cannot get credit for courses with an undergraduate number (4999 and lower), a graduate number (5000 or higher) is needed to accommodate them. But tuition is higher for graduate-numbered courses than for undergraduate-numbered courses, so it's desirable to have an undergraduate number for the undergraduates wanting to take the course. Hence the piggy-back arrangement.
However, state accreditation rules prohibit the University from offering the same course under two different numbers, and therefore either the material covered or the requirements must be different for the two groups of students. So, in the syllabus, you will see that the 5404 students have some requirements that the 4402 students do not. Note that what matters for these purposes is only the course number you are registered under, not whether you actually are an undergraduate or graduate student.