Brooklyn Technical High School

 

VIDEO OVERVIEW OF MAJOR 

 

Introduction to Math Research: Students will be exposed to a variety of advanced topics in mathematics using an inquiry based pedagogical approach. Students will use professional journals and other sources to conduct expository and original research. Papers will be submitted to the NYC Metropolitan Math Fair as well as various other research competitions including but not limited to NYCSEF and Intel. 

 

Advanced Euclidean Geometry: Using Sketchpad as an investigative tool, students will explore: Elementary Euclidean Geometry, Concurrency of Lines in a Triangle, Collinearity of Points, Some Symmetric Points in a Triangle, Triangle Properties, Quadrilaterals, Equicircles, The Nine-Point Circle, Triangle Constructions, Circle Constructions, The Golden Section and Fibonacci Numbers.

 

Combinatorics: The three problems of combinatorics (existence, counting, optimization), basic counting rules, graph theory, generating functions, principles of inclusion and exclusion, pigeonhole principle, selected additional topics.

 

AP Physics/Calculus BC²*: This innovative triple period class will combine AP Calculus BC and AP Physics C. Students will work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. Students are expected to understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems; understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems; understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus; model a written description of a physical situation with a function, a differential equation, or an integral; use technology to help solve problems, experiment, interpret results, and verify conclusions; determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement; develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment. 

 

AP Statistics: The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: Exploring Data: Describing patterns and departures from patterns; Sampling and Experimentation: Planning and conducting a study; Anticipating Patterns: Exploring random phenomena using probability and simulation; Statistical Inference: Estimating population parameters and testing hypotheses.