Mathematics Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein Mathematics are well and good but nature keeps dragging us around by the nose. ~Albert Einstein

Math at HSMSE Every student at HSMSE... – Takes math every term – Has the opportunity to take AP Calculus or AP Statistics – Has the opportunity to participate in Math Team and do original math research – Gets a premier preparation for future mathematics, science, and engineering coursework in college

HSMSE Math Concentration What is MathCo? What courses will I take? What are the benefits of MathCo? What are the students saying about MathCo? What are MathCo students working on? Questions

What is MathCo ? An opportunity for students who like math to do more of it in their junior and senior years MathCo students add one math class each year at the expense of one engineering class MathCo students take 2 semesters of Math Team All students also take English, Social Studies, Science, PE, LOTE, and enrichment classes

Typical Schedule MathCo Junior Year A-dayB-day 8:00-9:25AP EnglishU.S. History 9:30-10:55PE / Physics LabAP Statistics 11:00-11:45Enrichment (e.g., Math Team) 11:50-12:35Lunch 12:40-2:05Principles of Engineering LOTE 2:10-3:35Physics Precalculus(Fall)/ Calculus(Spring)

Typical Schedule MathCo Senior Year A-dayB-day 8:00-9:25EnglishEconomics(Fall) / U.S. Gov't(Spring) 9:30-10:55PEAP Calculus BC 11:00-11:45Enrichment (e.g., Math Team) 11:50-12:35Lunch 12:40-2:05Advanced Science Advanced Math Topics

Key Differences in Courses What am I getting? AP Calculus and AP Statistics Advanced Math Topics Graph Theory, Number Theory, Game Theory, Problem- solving, Maple Minimum of 2 semesters of Math Team Not unique to MathCo What am I giving up? MathCo Juniors do not take Digital Electronics MathCo Seniors do not take the engineering elective

What are the benefits of MathCo? Make connections between areas of study Sharpen problem-solving skills Place additional emphasis on theoretical aspects and rigors of math Study advanced math topics not usually seen in high school Opportunity to earn AP credits in 2 subjects (AP Statistics results are available to include on college applications in fall of senior year.) More advanced placement in college math Opportunity to investigate/research math topics based on interest

What are the students saying about MathCo? “You get to both have fun and learn new, interesting, and cool topics.” “Math Concentration gives you the “I’m a genius” feeling.” “Math Concentration is an excellent chance to learn about the creative and less conventional areas of math that normal classes do not touch.” “…with Math, there are several ways to solve one problem. You learn how to look at things differently.” “Classes like Statistics and Discrete Mathematics push you to think critically rather than simply plugging numbers into functions.”

What are MathCo students working on? Viewing the world with an analytical eye Backing-up claims Making connections between statistics and calculus Presenting information and analysis Discussing mathematical ideas with other students and with staff Modeling phenomena Using advanced technical tools to analyze, explore, visualize and solve mathematical problems

Questions? (Here are some from the MathCo students) If a given number is cyclically prime, in what case is it also a permutation prime number? Find the volume of an n-dimensional cube formed from an interior n-dimensional sphere, tangent to 2n outer spheres, which are each tangent to n surfaces of the figure. How can modulo arithmetic be used to simplify and solve divisibility in quadratic equations? 25 bags are to be weighed 5 at a time. The scale puts the 5 bags in order from heaviest to lightest. Find the least number of times you’ll need to weigh the bags before you know the three top heaviest in order. Does an infinite series of the reciprocals of the Fibonacci sequence ever converge? If so, how fast?