200-Level Math Courses

Math 201 - An Introduction to Mathematical Writing (IBL)

Prerequisites:	Math 115 and intellectual curiosity
Credit:	1 Credit - This course is designed to be taken concurrently with Math 217
Content:	This is a course about the nuts and bolts of mathematical writing. The course introduces the fundamentals of mathematical communication (e.g., sets, functions, quantifiers) and explores various proof techniques (e.g., contrapositive, contradiction, induction). Most importantly, it provides guided practice in rudimentary proof writing. Topics include elementary set theory, functions, existential and universal quantifiers, and proof techniques. The course has no lecture; students work through the worksheets in groups.

Prerequisites:

Math 115 and intellectual curiosity

Credit:

1 Credit - This course is designed to be taken concurrently with Math 217

Content:

This is a course about the nuts and bolts of mathematical writing. The course introduces the fundamentals of mathematical communication (e.g., sets, functions, quantifiers) and explores various proof techniques (e.g., contrapositive, contradiction, induction). Most importantly, it provides guided practice in rudimentary proof writing. Topics include elementary set theory, functions, existential and universal quantifiers, and proof techniques.

The course has no lecture; students work through the worksheets in groups.

Math 205 - Calculus of Several Variables

Prerequisites:	Math 116, 156, 186, 276 or 296
Credit:	4 Credits. No credits after 215 or 285
Background and Goals:	This is a multivariable calculus course that is an alternative to Math 215 for students intending to concentrate in Math, Stats, or the Social Sciences. Topics covered included graphs, limits, continuity, and partial derivatives of functions of several variables; vectors; optimization including Lagrange multipliers; line and volume integrals; and Green's Theorem.
Content:	Topics covered include vector algebra and vector functions; basic matrix operations; basic analytic geometry of planes, surfaces, and solids; funtions of several variables, including partial differentiation, gradients, differentials, two variable Taylor polynomials of degrees one and two, and constrained and unconstrained optimization; epsilon-delta definitions of limits, continuity, and differentiability of functions of several variables; line and volumes integrals and applications; vector fields; and Green's Theorem. The course includes regular use of mathematical software for visualization. The focus in general is on concepts and solving problems rather than theory and proof. Conncections to familiar concepts from single variable calculus and multivariable applications to probaility and economics are emphasized.

Math 214 - Applied Linear Algebra

Prerequisites:	Math 116, 156, 186, 276, or 296
Credit:	4 Credits. No credit granted to those who have completed or are enrolled in Math 217, 417, 419, or 420.
Background and Goals:	An introduction to matrices and linear algebra. This course covers the basics needed to understand a wide variety of applications that use the ideas of linear algebra, from linear programming to mathematical economics. The emphasis is on concepts and problem solving. The sequence 214-215 is not for math majors. It is designed as an alternate to the sequence 215-216 for engineering students who need more linear algebra and less differential equations background.
Content:	An introduction to the main concepts of linear algebra… matrix operations, echelon form, solution of systems of linear equations, Euclidean vector spaces, linear combinations, independence and spans of sets of vectors in Euclidean space, eigenvectors and eigenvalues, similarity theory. There are applications to discrete Markov processes, linear programming, and solutions of linear differential equations with constant coefficients.

Math 215 - Multivariable & Vector Calculus

Prerequisites:	Math 116, 156, 186, 276, or 296
Credit:	4 Credits. Credit is granted for only one course among Math 215 and 285. 2 credits after 205.
Background and Goals:	The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to concentrate in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.
Content:	Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green’s Theorem, Stokes’ Theorem, and Gauss' Theorem. There is a weekly computer lab.

Math 216 - Introduction to Differential Equations

Prerequisites:	Math 116, 156, 186, 276, or 296
Credits:	4 Credits. Credit is granted for only one course among Math 216, 286, and 316.
Background and Goals:	For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations: 216&417 (or 419) and 217&316. The sequence 216&417 emphasizes problem-solving and applications and is intended for students of engineering and the sciences. Mathematics majors and other students who have some interest in the theory of mathematics should elect the sequence 217&316.
Content:	Math 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace trans- form techniques.

Math 217 - Linear Algebra

Prerequisites:	Math 215 or 285 or 205
Credit:	4 Credits. No credit granted to those who have completed or are enrolled in Math 419 or 420. 2 credits granted to those who have completed Math 214 or 417.
Background and Goals:	For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations: Math 216 & 417 (or 419) and Math 217 & 316. The sequence 216 & 417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Mathematics majors and other students who have some interest in the theory of mathematics should elect the sequence 217 & 316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.
Content:	The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be an emphasis on the concepts, logic, and methods of theoretical mathematics.

Math 275 - Introduction to Cryptology (IBL)

Prerequisites:	Math 115 or AP
Credit:	4 Credits. No credit granted to those who have completed any prior introduction to proof math course (e.g., 185, 186, 217) with a grade of C or higher. No credit granted to those who have completed any 300 level or higher Mathematics course other than 310, 385, 489.
Background and Goals:	This course studies cryptography and number theory with the additional goal of introducing students to the art of writing proofs. This is an Inquiry Based Learning course that stresses discovery as a vehicle for learning. Students will be required to work in groups and experiment in class. Grades will be based on worksheets, homework and class participation, with a strong emphasis on homework.
Content:	This course introduces modern cryptology, including the Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the TSA cryptosystem, and digital signatures. Along the way, the course introduces many of the mathematical ideas involved in the development and analysis of cryptography systems. Mathematical topics include primality testing, factorization algorithms, probability theory, statistics, and enumeration. Throughout the course students will work on effectively communicating mathematics, both written and orally. Moreover, students will develop rigorous mathematical proof writing skills, and a primary goal of the course is to not only understand how various cryptosystems work, but why.

Math 276 - Explorations in Calculus (IBL)

Prerequisites:	Math 115 or AP Credit or permission of math advisor; highly recommended for students who have taken Math 275
Credit:	4 Credits. Credit is granted for either Math 276 or 186, but not both
Background and Goals:	This course is an Inquiry-Based version of Honors Calculus I and II (such as Math 185/186) and provides the necessary preparation for Multivariable Calculus (Math 215 or the honors version, Math 285). A student who has had some exposure to calculus (e.g., AB or BC in high school, or Math 115) and proof writing (e.g., Math 201 or Math 275) will be well-prepared for this course. The majority of class time will be spent working in groups and presenting ideas and solutions to problems.
Content:	This is a calculus course from a theoretical perspective. The main emphasis is on learning how to write rigorous proofs for topics the students are probably already familiar with. The main mathematical topics include sequences and series of real numbers, complex numbers, properties of the real line, continuity and limits of real functions, differentiation, and integration.

Math 285 - Honors Multivariable & Vector Calculus (IBL)

Prerequisites:	Math 156, 186, 276, or permission of honors advisor
Credit:	4 Credits. Credit is granted for only one course among Math 215 and 285. 2 credits after 205.
Background and Goals:	The sequence Math 185-186-285-286 is an introduction to calculus at the honors level. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LS&A Honors Program.
Content:	Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation, maximum-minimum problems; line, surface, and volume integrals and applications; vector fields and integration; curl, divergence, and gradient; Green’s Theorem and Stokes’ Theorem. Additional topics may be added at the discretion of the instructor.

Math 286 - Honors Differential Equations

Prerequisites:	Math 285 or permission of instructor
Credit:	3 Credits. Credit is granted for only one course among Math 216, 286, and 316.
Background and Goals:	The sequence Math 185-186-285-286 is an introduction to calculus at the honors level. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LS&A Honors Program.
Content:	Topics include first-order differential equations, higher-order linear differential equations with constant coeffi cients, an introduction to linear algebra, linear systems, the Laplace Transform, series solutions, and other numerical methods (Euler, Runge-Kutta). If time permits, Picard’s Theorem will be proved.

Math 289 - Problem Solving

Prerequisites:	None.
Credit:	1 Credit. May be repeated for credit
Background and Goals:	One of the better ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. This course is intended for students who are enthusiastic about doing mathematics and solving challenging problems. It is not restricted to honors students. This course is excellent preparation for the Putnam competition.
Content:	Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students.

Math 295 - Honors Mathematics I

Prerequisites:	Permission of honors math advisor
Credit:	4 Credits.
Background and Goals:	Math 295-296-395-396 is the most theoretical and demanding honors math sequence. The emphasis is on concepts, problem solving, as well as the underlying theory and proofs of important results. It provides an excellent background for advanced courses in mathematics. The expected background is high school trigonometry and algebra (previous calculus is not required, but is helpful.) This sequence is not restricted to students enrolled in the LS&A Honors program. Math 295 and 296 may be substituted for any Math 451 requirement. Math 296 and 395 may be substituted for any Math 217 requirement.
Content:	Axioms of the real numbers, completeness and connectedness in the real line. Functions of a real variable, limits and continuity, uniform continuity, extreme and intermediate value theorems, differentiation, integration, the fundamental theorem of calculus, Taylor's theorem with remainder.

Math 296 - Honors Mathematics II

Prerequisites:	Math 295
Credit:	4 Credits.
Background and Goals:	Math 295-296-395-396 is the most theoretical and demanding honors calculus sequence. The emphasis is on concepts, problem solving, as well as the underlying theory and proofs of important results. It provides an excellent background for advanced courses in mathematics. The expected background is high school trigonometry and algebra (previous calculus is not required, but is helpful.) This sequence is not restricted to students enrolled in the LS&A Honors program. Math 295 and 296 may be substituted for any Math 451 requirement. Math 296 and 395 may be substituted for any Math 217 requirement.
Content:	Sequences and series of functions, power series, uniform convergence, real analytic functions. Vector spaces, bases, linear transformations, dual spaces, determinants, traces, eigenvalues, inner-product spaces, spectral theory. Limits and continuity in Euclidean space, derivative as a linear map, Chain Rule, inverse/implicit function theorems.

Math 297 - Introduction to Analysis (IBL)

Prerequisites:	Math 217
Credit:	4 Credits.
Background and Goals:	This is a course in analysis for students who know how to write rigorous mathematical arguments and possess a firm understanding of the standard concepts of linear algebra. It is specifically designed for students who excelled in Math 217, love mathematics, and wish to transition into the Honors Analysis Sequence. Math 297 may be substituted for any Math 451 requirement.
Content:	This is a course in real analysis for students possessing both a firm understanding of how to read and write rigorous mathematical arguments and a solid understanding of the standard concepts of linear algebra at the level of Math 217. Topics covered include: axioms of the real numbers; complete-ness, compactness, and connectedness for finite dimensional inner product spaces; sequences, series, and limits in inner product spaces; continuity and uniform continuity for functions of finite dimensional inner product spaces; the extreme and intermediate value theorems, differentiation, integration, the fundamental theorem of calculus, and Taylor's theorem with remainder for functions of one real variable. The emphasis is on concepts, problem solving, and the underlying theory and proofs. It provides an excellent background for advanced courses in mathematics.

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