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Paul Zorn
President,
Mathematical Association of America
Department of Mathematics, Statistics, and Computer Science
St. Olaf College
1520 St. Olaf Avenue
Northfield, Minnesota 55057-1098
Phone: 507-786-3414
Fax: 507-786-3116
Email: zorn@stolaf.edu
Office: Regents Hall of Mathematical Sciences 508
Courses I'm teaching in 2010-11
- Multivariable calculus:
What's it about?
Multivariable calculus (MVC) differs from single-variable calculus (SVC)
mainly in that, while SVC has to do with derivatives and integrals of
real-valued functions of one variable, MVC methods allow us to
treat functions of several variables. The difference may
not seem like much; in fact, it's huge. The real world involves
many, many variables, and so MVC methods let us study and model more
real-world phenomena, and in more detail, than would be possible with SVC
methods alone.
- Elementary real analysis :
What's it about?
The very short answer is that real analysis is the mathematical theory
behind elementary calculus. A slightly longer answer is that mathematical
analysis is the branch of mathematics that deals with properties of
functions. (In the same drastically oversimplified sense, the other two
main branches of mathematics are algebra - having to with
equations - and arithmetic - having to do with
numbers . The ``real'' in real analysis has to do with the real
numbers: the functions studied in real analysis are usually
real-valued functions of a real number. One important purpose
of the course is to revisit - a lot more carefully than on the first pass
- important ideas, definitions, and theorems from elementary calculus.
- Complex analysis:
What's it about?
To make a long story very, very short ... :
Mathematical analysis is the branch of
mathematics that deals with properties of
functions. (In the same drastically
oversimplified sense, the other two main branches of mathematics
are algebra --- having to with equations -- and
arithmetic ---having to do with numbers .
The ``complex'' in complex analysis has to do with the complex numbers: just
as the functions studied in real analysis are
usually real-valued functions of a real number,
the functions studied in complex analysis are
usually complex-valued functions of a complex number.
Interestingly enough, many of the familiar functions, operations,
and ideas from real analysis carry over (with appropriate changes)
to complex analysis: polynomials, trigonometric functions, logarithms,
derivatives, integrals, etc. In a sense, therefore,
this course is really about old, familiar ideas---but seen from a
new and different point of view.
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