### Session Descriptions

Each session lasts for 90 minutes. The presented material will consume about 60 minutes, and the remaining
time is reserved for questions of all kinds

### Algebra, Parts 1 and 2

by John Boller

Basic Algebra encompasses a vast array of definitions,
formulas, and techniques, all of which are necessary
for progress in later mathematics courses. In these
sessions, we review many of the basic skills while
justifying their use, and try to provide a rationale
for categorizing this large quantity of information.

### Don’t Go It Alone: Using Math Help Resources Effectively

by Derek Bruff

So you’ll go to class, pay attention, take careful notes, and do your
homework. You might do well in your college math class this way, but why
not take advantage of all the math help resources available to you?

In this session, we’ll provide smart strategies for getting help in your
math class, including getting the most out of your textbook, why and how to
talk to your instructor outside of class, how to get assistance from your
course assistant, and why it’s so important to work with your classmates on
your homework.

### Conic Sections

by Matthew Leingang

The Conic Sections (circles, ellipses, parabolas, and hyperbolas) have been
studied since the time of the Greeks. We'll look at each of these curves, learn how to
identify it by its equation, find what elements of the equation describe their shape,
and how they are geometrically defined.

In the end, we'll understand what cones have to do with it at all as well!

### Trigonometry: More than Just SOHCAHTOA

by Derek Bruff

Students sometimes see trigonometry as an unreasonably large collection of
equations and identities. However, there’s a bigger picture behind all of
those details, and we’ll explore that bigger picture in this session. We’ll
look at the unit circle, the six basic trig functions (sine, cosine,
tangent, and the rest), angles and radians, triangles (right and otherwise),
inverse trig functions, and, yeah, some equations and identities, too.

Trigonometric functions are some of the important functions studied in
calculus. This trig refresher session will be a good review for those who
have studied trig but might be a little rusty going into calculus.

### Modeling real life applications in biology and economics

by Thomas Judson

Modeling is the application of mathematics to real-worl problems. We'll talk
about the Gini index for measuring the inequity of an economy, the spread of infectious
diseases, and how the HIV virus evolves within the human body.

The rest of the time will be devoted to course selection advice for students interested
in concentrating in biology or economics.

### Complex Numbers

by Oliver Knill

"The shortest path between two truths in the real domain passes through
the complex domain."

Jacques Hadamard (1865-1963). Hadamard and Vallee Poussin were the first to prove
the prime number theorem (using complex numbers or course)

"This is the most remarkable formula in Mathematics."

Richard Feynman (1918-1988). Feynman worked on quantum-electrodynamics
and won the physics Nobel price in 1965

"Gentlemen, that is surely true, it is absolutely paradoxical;
we cannot understand it, and we don't know what it means. But we have proved
it, and therefore, we know it is the truth."

Benjamin Peirce (1809-1880), the "first true American mathematician".
Professor at Harvard who worked in celestial mechanics,
number theory and algebra.

"The natural numbers are the most complex numbers.
The complex numbers are the most natural numbers."

Jacques Tits, (1930- )
Tits is a Belgian mathematician, who won the Wolf prize
in 1993.

### Using Technology

by Matthew Leingang

We'll look at your graphing calculator (if you already have one) and how to use it. We'll also examine some of the most powerful mathematics software packages out there, Mathematica and Matlab. Both of these are available to all Harvard College students thanks to our site license.