This is the first half of a university-level course in multivariable calculus. This course includes the theory and application of vector functions and partial derivatives. Topics include basic operations with vectors and parametric curves in 2- and 3-space, the Frenet Frame and Frenet-Serret equations, continuity and differentiability of functions of several variables, gradients and directional derivatives, and classic optimization problems. Additional topics and projects will be added throughout the course to explore interesting applications of calculus and differential equations. This is one part of a 2-semester course sequence (MA4064 and MA4066). Students must enroll in both semesters when registering. Once enrolled students may not drop a single semester without approval from the Dean of Mathematics.

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Students will continue their study of multivariable calculus including multiple integrals, the Jacobian and change of variables, vector fields, line and surface integrals, divergence and curl. Significant time is devoted to the study of Green's Theorem, Stokes' Theorem and the Divergence Theorem. Students will be expected to use formal mathematical proofs and to work on extended problem sets. Additional topics and projects will be added throughout the course to explore interesting applications of calculus and differential equations.

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This course combines three perspectives: inferential thinking, computational thinking, and real-world relevance. Given data arising from some real-world phenomenon, how does one analyze that data so as to understand that phenomenon? The course teaches critical concepts and skills in computer programming and statistical inference, in conjunction with hands-on analysis of real-world datasets, including economic data, document collections, geographical data, and social networks. It delves into social issues surrounding data analysis such as privacy and design.

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This course introduces students to cryptographic methods used to encipher and decipher secret messages with an emphasis on using computer programming to automate the process. Through class discussions, problem solving, group activities, and programming assignments, students will learn a variety of encryption schemes ranging from the age of Caesar to modern public key encryption used to secure digital communications online. Students will learn introductory number theory and statistics to describe these methods and identify weaknesses that allow secret messages to be read without the key. Students will also learn programming topics such as variables, functions, conditional logic, looping, and file input/output in the Python language to implement each cryptographic method. This course will utilize a blended learning environment with large portions of material being taught online and utilizing in class time for working in groups.

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This course offers students an overview of a number of applications of mathematics, especially those topics that relate to the concept of fair and just relations between the individual and society. Topics covered include fair division of resources and costs, voting methods, apportionment of legislative bodies, power of voting coalitions, and introductory graph theory. The course will also extend students' knowledge of matrices and their use in applications related to the social sciences. 

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