GAME THEORY, DECISION MAKING, AND OPTIMIZATION |
FINANCIAL AND ACTUARIAL MATHEMATICS |
Recommended co-requisite: AP Calculus AB or AP Calculus BC
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Recommended co-requisite: Calculus
Required pre or co-requisite: AP Statistics |
Game theory is a field of mathematics that deals with strategies in competitive situations. It is used extensively in economics, finance, political science, and even in fields such as biology. In a way, it can be seen as mathematical psychology, as we will try to use mathematics to model behavior.
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Actuaries are consistently ranked among the happiest people in their profession, yet very few people have even heard of the word! This course is intended to introduce students to the profession, especially the mathematics required to become a successful Actuary.
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This course will be split into two major interrelated components. The first will be traditional game theory. In this part, we will cover topics ranging from elementary game theory (static with perfect information), to more advanced topics (extensive/dynamic with imperfect information). We will also discuss issues such as trust and fairness. The second will be mathematical modeling with a focus on economics, decision-making, and optimization. Students will learn how agents (individuals, firms, countries, etc.) make decisions when it comes to consumption and production, especially in the face of uncertainty.
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From learning about fundamental concepts and applications of financial mathematics, to applying probability and statistics to assess risk, this course will open your eyes to a great career opportunity. This course will be split into two major components. The first will focus on financial concepts such as present and accumulated value of cash flows, and the concept of asset/liability management.
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This course is for students with an interest in business, economics, psychology, and behavior analysis. Students will use a wide range of mathematics, from basic algebra to calculus. They will develop skills in analysis and justification as they learn different mathematical models. By the end of this course, students will have an advanced understanding of game theory, economics, and mathematical modeling.
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The second will focus on using probability distributions to predict when events (good or bad) might occur in a business situation. For example, insurance companies may hire an Actuary to predict future payouts, timing of claims, or how many claims within a given period of time.
This course will arm students with the proper tools to manage risk through mathematical and statistical modeling.
Now accredited by St. John's University
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ALGORITHMSALGORITHMS are everywhere. They play the stock market, decide whether you can have a mortgage and may one day drive your car for you. Even Google is an algorithm – a search Algorithm. Algorithms are recipes for solving computational problems.
Algorithms is for students with an interest in theoretical computer science. There will be a heavy emphasis on proof, as students will analyze the effectiveness and efficiency of the algorithms presented and the algorithms created. In this course we will study fundamental algorithms for solving a variety of problems, including sorting, searching and graph algorithms. More importantly, we will focus on general design and analysis techniques that underlie these algorithms. Students will also learn to implement data structures, which help us to organize large amounts of information, and develop the algorithms necessary to build and maintain them.
Students will gain practical skills in problem solving and project management, as well as preparation for the USA Computing Olympiad.
Python will be used to illustrate and compare the various algorithms.
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C++ PROGRAMMING WITH APPLICATIONS IN FINANCERecommended co-requisite: AP-Computer Science-A
C++ is arguably the most important of the programming languages given its run time efficiency, access to hardware level functionality and the profligacy of well optimized libraries. C++ is the language of choice in any real time environment and therefore has huge applications in the Wall Street banks besides other enterprise applications. C++ provides a distinct competitive advantage to participants in coding competitions like the USA computing competition. Knowledge of C++ will boost the prospects of anyone serious about pursuing a career in engineering or computer science. This course provides in-depth coverage of object-oriented programming principles and techniques using C++. Topics include classes, overloading, data abstraction, information hiding, encapsulation, inheritance, polymorphism, file processing, templates, exceptions, container classes, and low-level language features like pointers. Additionally this course also teaches students about symbolic computing in Mathematica. Mathematica can generate code in C which can be embedded in C++ applications.
Students will gain practical skills in problem solving as well as preparation for the USA Computing Olympiad.
As capstone project, students will learn how to write real life applications for the financial industry. These projects will include trading simulations, and financial derivative pricing.
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MATHEMATICAL APPLICATIONS IN ENGINEERINGMathematical Applications in Engineering introduces students to the real-life applications of mathematics in the world of engineering. This course is designed to connect specific mathematical concepts learned throughout junior & senior years to structural engineering, finite element analysis, optimization, and computing.
Finite Element Analysis is a relatively new discipline in engineering allowing for efficient problem-solving techniques that previously were difficult or impossible to perform. Increasingly more engineering firms are implementing Finite Element Analysis to solve complex real-life problems in a simple and systematic way.
Students will also apply vectors and matrices for Matlab computing language to analyze truss-bridges. Since this course requires Calculus as a corequisite, derivatives and integrals are being utilized in the second semester of this course to calculate loading conditions & internal behaviors of structures.
At the end of this course, students will have acquired all the necessary knowledge and experience to embark in a career of engineering and to be part of improving human civilization.
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