Calculus Adjacent

8/10/2019 Calculus Adjacent

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Calculus AdjacentDesigning Math Elective Accessible to All


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Background


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Assumptions


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MyAssumptionis

Math electives are currently oat your school

or

There is a strong probability th

they will be offered sometimenear future.


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Reality Check So, why are you here exactly?


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The TypicalMath ClassSequence

Algebra 1 Geomet

AlgebraPre-Calculus

Calculusand/or

Statistics

Maybe SOther St


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The Bay WayOur Philosophy


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An AnnualProcess


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CourseOfferings

Cryptography

Applied ProbabilityTopology

Seminar in IndependentMathematical Study

Game Theory

Probability & Simulation


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Cryptography

How do we build and break codes? How haencoded and decoded information in the pit so difficult to crack someone elses code?trimester course takes an in-depth look at t

science of secret writing. Students explorecryptography through its history and in praattention to both the military and social dimcryptology and the public-policy questions encrypted information transmitted over thThe focus throughout the course is on the u

mathematics to create and analyze encrypalgorithms using a variety of mathematicaas frequency analysis, modular arithmetic, theory and one- and two-way functions. Thfollows The Code Book by Simon Singh.

Prerequisite: Math 3.


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SampleProblem

BT JPX RMLX PCUV AMLX ICVJP IBTWXVLMTR PMTN, MTN YVCJX CDXV MWMBTAMTNGXRJBAH UQCT JPX QGMRJXV CI JJPX HBTWR QMGMAX; MTN JPX HBTW

QMVJ CI JPX PMTN JPMJ YVCJX. JPXT JPXACUTJXTMTAX YMR APMTWXN, MTN PBJPCUWPJR JVCUFGXN PBL, RC JPMJ JPX PBR GCBTR YXVX GCCRXN, MTN PBR HTCTX MWMBTRJ MTCJPXV. JPX HBTW AV

MGCUN JC FVBTW BT JPX MRJVCGCWXVAPMGNXMTR, MTN JPX RCCJPRMEXVR.HBTW RQMHX, MTN RMBN JC JPX YBRXFMFEGCT, YPCRCXDXV RPMGG VXMN JPYVBJBTW, MTN RPCY LX JPX BTJXVQVXJPXVXCI, RPMGG FX AGCJPXN YBJP RAM


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AppliedProbability

The ability to think probabilistically is a fundacomponent in the sciences and social sciencetrimester course introduces students to the rmodels, skills, and tools, by combining math

conceptual understanding and intuition. Studon modeling, quantification and the analysisuncertainty. Actual applications are the empcourse; little emphasis will be placed on prooApplications from many disciplines, such as esociology, psychology, political science as we

hard sciences form a fundamental part of thistudying topics that range from simple gameto the more advanced game theory models, behavioral economics, students attempt to mof the randomness in their world.



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SampleProblem

A company has a production facility that decide if they are going to filter their wasbefore dumping it into the local water sup

will cost them $25,000 per year or they just dump the unclean waste into the watsupply. If they get caught dumping polluwater supply they will be fined $500,000. company knows the government only haof people inspectors to check on compan

estimate there is only a 10% chance they caught if they choose not to filter. The coowns 100 such facilities and must decide going to add filters to all of them or nonethem. What should they do?


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Topology

Topology is the mathematical study of shapespaces. Bowls and plates, for example, sharetopological categorization, but a coffee mugbecause of the hole made by the handle. In fatopology, squares, rectangles, parallelogramtrapezoids, and circles are all considered to bTopology is the branch of mathematics creatignoring things like size and angle. But heresquestion: if one ignores these ways of measucan one tell when two shapes are different? Senrolled in this one-trimester course examinlike this. They also explore shapes like the Mothe Klein bottle, the torus, and ideas about gorientability, and dimension, including ways the fourth dimension. [This course is consideHonors course; see page 34 for more informa



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SampleProblem

Dr. A. Square shocked the citizens of Flatland wtraveled due north from Flatsburgh (the capitala blue thread behind her and, after many montto Flatland from the south. Everyone concluded

Flatland must be a sphere. Dr. Square became ahero and the blue thread was kept in place as a monument.

The next year, Dr. Square decided to celebrate circumnavigating triumph by setting out again Flatsburgh, this time travelling due East and tra

thread. After many months, she arrived at Flatsthe west as expected, however a new mystery asecond circumnavigation, Dr. Square never encblue thread.

Can Flatland indeed be a sphere? Explain. Dillustrate some possible shapes for Flatland


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Game Theory

To a game-theoretician, agameis a situation wheentities compete for limited resources. Game thethe mathematical study of these games, the anacharacteristics of a given game to determine the strategy for the players involved. This course is tin strategy: how does one create a winning plan oones resources, information, and opponents? Cocourse will emerge entirely through the study of and competitive situations. In addition to relativgames, we will spend a great deal of time applyintheory to economics, business, evolutionary biolo

and voting, military strategy, psychology, philosoand international relations. The culminating activcourse will be a project in which students use thetools of game theory to build a strategy for a comof their own choosing.

Prerequisite: successful completion of Math 2.


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SampleProblem

The Ultimatum Game: A common psychology eultimatum game involves two players, who play Player A is given an amount of money, say $10. Hto split it into two nonzero parts, of any magnitu

offer one of the parts to Player B. If Player B acceoffer, then they each keep their portions of the prejects Player As offer, the game ends and no onany money. For the sake of our analysis, supposemust split the sum into whole-dollar increments

1. Find at least 3 distinct ways of clearly and conciselinformation in the game description above.

2. What are the optimal strategies for Player A and Pcase? What will the outcome be if both players plastrategies?

3. Read the scientific paper at this link:http://www.psych.ubc.ca/~henrich/Website/Paperdetermine what it says about how effectively (fromperspective) different societies play this game.
http://www.psych.ubc.ca/~henrich/Website/Papers/ult.pdfhttp://www.psych.ubc.ca/~henrich/Website/Papers/ult.pdfhttp://www.psych.ubc.ca/~henrich/Website/Papers/ult.pdf


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Seminar inIndependentMathematical

Study

Each student in this one-trimester course will spend the term mathematical topic of his or her choosing (with instructor appwill take place both during the regularly scheduled class meetoutside of class for homework. In addition, students will presethe class periodically throughout the term, keep a written "woprogress, have regular one-on-one meetings with the teacherchecks, write and solve problem sets related to their topic of s

a final paper and presentation for the class at the end of the tewill be scheduled for either the winter or spring term. In the tecourse begins, students will be asked to do a nontrivial amounwork in order to help the instructor prepare the course and locmaterials. This preliminary work is not optional; students whoit in a timely manner may be dropped from the course at the idiscretion. This course is significantly different from other Baycourses in that students will not work collaboratively with theregular basis. Instead, they will pursue individual study of a toavailable in print or online. The teacher may provide assistancbut the intent of this course is to be an independent study, notutorial. In order to be successful in this class, students must band intellectually independent, self-motivated, persistent, anstudent who possesses these qualities is encouraged to apply However, in the Bay School math curriculum, these qualities amost fully and intentionally in Analysis of Functions. Analysis prerequisite for the course, but students who have not yet comshould be aware that Math 1, Math 2, and Math 3 do not targemind as specifically as Analysis does.

Prerequisite: instructor permission.


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ProposedCourses(that have

not run)

Analytic Geometry

History of Math

Probability & Decision-Making

The Mathematics of Social Choice

Euclidean and Non-Euclidean GeoFractal Geometry


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Your Ideas What Math elective(s) would you lik

Calculus Adjacent

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