MATHEMATICS

 

PTI has an extensive math curriculum ranging from Pre-Algebra to advanced courses in statistics and even, from time to time, calculus. Our faculty come from various departments within Princeton and Rutgers, with backgrounds in math, applied science, social science and engineering. Instructors teach core math skills while emphasizing real-world applications of algebra and statistics with examples drawn from diverse fields like sociology, engineering and astrophysics. Our objective as teachers is to help students become comfortable with core concepts from algebra and statistics while enhancing awareness of how math is used in everyday life.

​

The math curriculum encompasses preparatory classes in addition to college courses. The introductory sequence of pre-Algebra (MAT033) and Beginning Algebra (MAT037), introduce key mathematical concepts such as positive and negative numbers, order of operations and algebraic expressions. These courses also help students to become familiar with the terminology and symbols commonly used in the study of mathematics. Students who have completed these courses may later enroll in Intermediate Algebra with Applications (MAT135) and College Algebra with Applications (MAT140). These courses focus on problem solving and emphasize the ability to convert abstract concepts into mathematical expressions.

​

Upon completing the MAT033/037 sequence, students can also continue on to a comprehensive statistics sequence consisting of Elementary Statistics I (MAT125) and Elementary Statistics II (MAT126). These courses cover statistics in great detail, starting with the basics of probability theory and continuing through hypothesis testing.

The most advanced mathematics courses offered through PTI are Pre-Calculus (MAT146) and Calculus (MAT151). Pre-Calculus focuses on manipulating functions that are important in the study of calculus, including polynomial, logarithmic, exponential and trigonometric functions. It also introduces problem-solving strategies that are important in calculus, including graphing expressions, finding roots of functions and simplifying complex functions.  Calculus I (MAT151) emphasizes core capabilities in calculus such as taking limits and differentiating or integrating mathematical expressions.

 

 

 

MAT033: Pre-Algebra

This is considered a foundation course in mathematics, which prepares students for MAT100-level courses. In MAT033, students learn the basics of practical arithmetic and geometry, including numbers, decimals and percents, fractions, exponents, basic graphing, and geometry. This course also introduces key concepts in algebra such as variables and equations. MAT033 also helps students to become familiar and comfortable with the terminology and notation frequently used in the study of mathematics.

 

​

​

MAT037: Beginning Algebra

This course is designed for students with some prior experience in algebra who may benefit from a refresher course to help strengthen and reinforce their understanding of the fundamentals like arithmetic, basic expressions and variables. Topics covered in this course include exponential and polynomial expressions, as well as techniques for manipulating these expressions such as factoring. Students also learn to graph various types of linear and nonlinear expressions. Throughout the course, students learn to read and analyze word problems, converting written information into meaningful mathematical expressions. This includes defining appropriate variables and expressing the relationships between them in valid mathematical equations.

 

 

​

MAT 125/126: Elementary Statistics I/II

This is a two-course sequence in statistics. MAT125 and deals with the key concepts and methods of probability and statistics, from probability theory to modeling and errors. Topics covered include basic probability, probability distributions, permutations and combinations, conditional probability and statistical inference. This course also introduces Bayes' theorem and the concepts of sampling, sampling error, means and dispersions, and correlation. MAT126 focuses on the analysis of variance, i.e. the use of statistical methods to determination differences among populations. This includes a discussion of the misuses of statistics. Observational and experimental data are discussed, along with techniques for visualizing (i.e. graphs, tables) and summarizing (i.e. means and standard deviations) data. The course goes into more depth on sampling and the central limit theorem. Hypothesis testing also makes up a large portion of the course, with an emphasis on understanding the concept of statistical significance. This is reinforced with real-world examples involving datasets that are relevant to fields ranging from sociology to astrophysics. Throughout MAT125 and MAT126, the terminology and notation used in the study of statistics is introduced and reinforced. Students are taught to interpret statistical information and apply concepts from probability theory and statistics. An emphasis is placed on reading and interpreting word problems, defining appropriate variables, understanding potential sources of bias, and knowing how and when to apply various tests for statistical significance.

 

 

 

MAT135/140: Intermediate/College Algebra with Applications

This is a two-course sequence in Algebra. MAT135 introduces important concepts in Algebra, including function notation, linear, quadratic, and absolute value functions and equations as well as complex numbers. Also covered are rational expressions and equations; rational exponents and equations; radicals and radical equations. Students learn to solve linear and nonlinear equations in one or two variables. This includes studying techniques to simplify expressions, such as factoring and polynomial division. Data visualization techniques like graphing functions and interpreting data that is presented visually in graphs or tables are also covered. MAT140 builds on the concepts taught in MAT135 and applies them to functions that are relevant in real-world science and engineering problems, including linear, exponential, logarithmic, polynomial and rational functions. Students learn to recognize and solve problems involving these types of functions. Various analytical methods for solving problems involving linear and nonlinear functions are covered. An emphasis is placed on reading, interpreting and solving word problems, which highlights the real-world applications of the concepts taught in these courses.

 

 

 

MAT146: Pre-calculus

The two primary goals of MAT146 are 1) to prepare students for calculus, and 2) to develop a comprehensive understanding that functions are statements of how a change in one quantity brings about a change in another quantity. Through this course, students develop quantitative and logical skills that will allow them effectively interpret and communicate mathematical problems and results, both in abstract and contextual settings that arise in everyday life.

MAT146 includes an in-depth study of polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions, expressions, equations and identities. Students are taught to visualize and interpret the graphs of these functions as well. Graphical and algebraic techniques for solving complex problems involving one or more equations are also discussed. The concept of generating mathematical models based on first-principles knowledge and/or data is also introduced, and students learn to apply such models to make predictions. Throughout the course, an emphasis is placed on the role that mathematics plays various fields.  This is reinforced through word problems drawn from fields of study such as physics and engineering.

 

 

 

MAT151: Calculus I

This course deals with the calculus of single-variable functions, discussing both differential and integral calculus and the relationship between them. Topics covered include differentiation of algebraic, exponential, logarithmic, trigonometric, hyperbolic, and inverse trigonometric functions. Various applications are also demonstrated, include curve sketching, relative rates, maxima, minima, and approximations. Students are also introduced to key techniques in calculus including differentiation and integration. This course also reinforces the important role that calculus plays in various science and engineering disciplines.