ESP Biography
CARLOS CORTEZ, ESP Teacher
Major: 18 College/Employer: MIT Year of Graduation: 2017 

Brief Biographical Sketch:
Not Available. Past Classes(Look at the class archive for more.)Knot Theory in HSSP Summer 2016 (Jul. 10, 2016)
This course will be an exposition to the beautiful subject of knot theory. While knot theory first attracted interest due to an outdated atomic model, it is now a central topic of study in lowdimensional topology with connections to several other fields. Furthermore, it is easy and fun to experiment with  we'll provide the string! However, you may be surprised at how difficult it is to tell if your friend's knot is the same as yours.
Topics will be tailored to the audience. Likely ones include: examples of knots and links, Reidemeister moves, prime knots, knot invariants (particularly knot polynomials), Seifert surfaces, braid groups. You may even learn a couple of party tricks and some knotsogreat puns!
Splay Trees (and other search tree fun) in Splash 2014 (Nov. 22  23, 2014)
Learn about splay trees: the elegant and effective selfadjusting binary search tree! Topics covered include the construction of the data structure, runtime analysis, and discussion of performance in practice. Also will briefly discuss the dynamic optimality conjecture if time allows.
Dissection problems in Splash 2014 (Nov. 22  23, 2014)
Can you cut a square in pieces and rearrange them to form an equilateral triangle of equal area? Of course!
Can you cut a cube in pieces and rearrange them to form a regular tetrahedron? Of course not!
Come to this class to learn: why you can cut and rearrange any polygon into another of equal area, but you can't do the same with polyhedra; why you can evenly cut sandwiches with as many as $$n$$ ingredients in $$n$$ dimensions in two equal parts with a single cut; and maybe even why you can cut one 3D ball into two identical copies of it.
For a demonstration, we may even have hamsandwiches. They'll be 3dimensional, we promise!
Olympiad Math Problem Solving in Splash! 2013 (Nov. 23  24, 2013)
This class will not be like your average high school math class. We will explore topics that include algebra, number theory, combinatorics, and geometry. The problems will range from advanced to math olymipad level and might include one or two International Math Olympiad problems.
