This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count
The design of algorithms is studied, according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time co
AP Physics C
This curriculum covers all of the material outlined by the College Board as necessary to prepare students to pass the AP Physics C exam. This course is designed to acquaint you with topics in mechanics and classical electricity and magnetism. The course covers two semesters. The first semester is devoted to Newtonian mechanics including: kinematics, laws of motion, work and energy, systems of particles, momentum, circular motion, oscillations, and gravitation. The second semester discusses the t
AP Physics B
This curriculum covers all of the material outlined by the College Board as necessary to prepare students to pass the AP Physics B exam. This course is divided into two semesters and is designed to acquaint you with topics in classical and modern physics. The first semester discusses topics in Newtonian mechanics including: kinematics, laws of motion, work and energy, systems of particles, momentum, circular motion, oscillations, and gravitation. The first semester concludes with topics in fluid
AP Calculus BC
This curriculum covers all of the material outlined by the College Board as necessary to prepare students to pass the AP Calculus BC exam. This course is divided into two semesters and is designed to acquaint you with calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. During this course you will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications.
AP Calculus AB
This curriculum covers all of the material outlined by the College Board as necessary to prepare students to pass the AP Calculus AB exam. This course is divided into two semesters and is designed to acquaint you with calculus principles such as derivatives, integrals, limits, approximation, and applications and modeling. During this course you will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications.
This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course in
This course introduces students to the basic concepts, logic, and issues involved in statistical reasoning. Major topics include exploratory data analysis, an introduction to research methods, probability, and statistical inference. The objectives of this course are to give students confidence in manipulating and drawing conclusions from data and provide them with a critical framework for evaluating study designs and results. An important feature of the course is the use of an intelligent tutori
Logic and Proofs is an introduction to modern symbolic logic. It provides a rigorous presentation of the syntax and semantics of sentential and predicate logic. However, the distinctive emphasis is on strategic argumentation. Students learn effective strategies for constructing natural deduction proofs. This learning is supported by the Carnegie Proof Lab: it provides a sophisticated interface, in which students can give arguments by strategically guided forward and backward steps.
Statics is a sophomore level engineering course, offered in all mechanical and civil engineering programs. Statics forms the essential pre-requisite to a number of follow-on courses, such as dynamics and mechanics of materials, and lays the foundation for design of mechanical systems. In most institutions, Statics is taught in a traditional way with an emphasis on the mathematical operations that are useful in its implementation, but without enough emphasis on modeling the interactions between r
Empirical Research Methods
Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl
The Introductory Economics course is a collection of online experiments and related on-line workbooks which can be used by individual learners or to supplement an instructor lead course. In each experiment a student is an active participant attempting to make deals with other traders in a market. After each experiment, the data the students generated is stored and the student will use this data to complete an online workbook. The workbook guides the student through the analysis and much of the e
Does excessive exposure to violent video games cause violent behavior? Does increased gun availability cause more crime or less? Causal claims permeate everyday life and are constantly the subject of "studies" reported in the newspaper. The material in Causal and Statistical Reasoning examines the nature of causal claims and the statistical sorts of evidence used to support them. The material is contained in: approximately 20 content modules, a repository of over 100 short case studies, and a "C
Highlight the meaning of a function, and see how it can be seen as something changing over time, with this tool that links a motion model to a graph.
Piecewise Linear Grapher
Highlight the language of domain and range, and the ideas of continuity and discontinuity, with this tool that links symbolic and graphic representations of each interval of a piecewise linear function.
Highlight the meaning of each component of a linear function's symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a line vertically or horizontally, rotating it around a fixed point, or reflecting it around the x- or y-axis.
Highlight the rationale behind symbolic operations used to solve a linear equation with this tool that displays changes in the graphic and area models of functions as you change the value of each symbolic element.
Highlight how changing a data set affects the mean, median, and mode with this tool (created by The Shodor Education Foundation and modified by The Concord Consortium) that allows you to add and delete data graphically.
Highlight the meaning of each component of a quadratic function's symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a parabola vertically or horizontally, dilating it, or reflecting it around the x- or y-axis.