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Course Syllabi

The syllabi for NetMath courses are listed below. Please note that more information about each course (tuition and fees, pre-requisites, policies, etc.) are listed in the individual course descriptions located under the Courses tab above.

## Math 112: College Algebra

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 112** offers a rapid review of basic techniques of factoring, rational expressions, equations and inequalities, functions and graphs, exponential and logarithm functions, polynomials, and the binomial theorem. This course uses the ALEKS assessment & learning system. Students who need both algebra and trigonometry should also enroll in MATH 114.

## Math 114: Trigonometry

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 114** covers degrees and radians, the trigonometric functions, identities and equations, inverse functions, oblique triangles, and applications. This course uses the ALEKS assessment & learning system. Credit is not given for both MATH 114 and either MATH 014 or MATH 115.

## Math 115: Precalculus

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 115** reviews trigonometric, rational, exponential, and logarithmic functions, and introduces finding the area under a curve. Intended for students who need preparation for MATH 220, either because they lack the content background or because they are not prepared for the rigor of a university calculus course. This course uses the ALEKS assessment & learning system. Credit is not given for both MATH 115 and either MATH 014 or MATH 114. Credit is not given for MATH 115 if credit for MATH 220 or MATH 221 has been earned.

## Math 220: Calculus I

**This course is currently under redevelopment. We expect to resume registrations during Fall 2023. **

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 220** is a standard first course in Calculus. Topics for this course include functions, limits, continuity, the derivative, differentiation of algebraic and trigonometric functions with applications including curve sketching, anti-differentiation and applications of integrals, the Riemann sum, and the Fundamental Theorem of Calculus.

## Math 231: Calculus II

**This course is currently under redevelopment. We expect to resume registrations during Fall 2023. **

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 231** is a standard second course in the Calculus sequence. Topics for this course include techniques and applications of integration, infinite sequences, power series, parametric equations, and an introduction to differential equations.

## Math 241: Calculus III

**This course is currently under redevelopment. We expect to resume registrations during Fall 2023. **

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 241** is a third course in Calculus and Analytical Geometry. Topics for this course include vector analysis, Euclidean space, partial differentiation, multiple integrals, line and surface integrals, and the integral theorems of vector calculus.

## Math 257: Linear Algebra with Computational Applications

**This course is currently under redevelopment. We expect to resume registrations during Fall 2023. **

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 257 **Introductory course incorporating linear algebra concepts with computational tools, with real world applications to science, engineering and data science. Topics include linear equations, matrix operations, vector spaces, linear transformations, eigenvalues, eigenvectors, inner products and norms, orthogonality, linear regression, equilibrium, linear dynamical systems and the singular value decomposition. Credit is not given for both MATH 257 and any of MATH 125, MATH 225, MATH 227, MATH 415 or ASRM 406

## Math 285: Differential Equations

**This course is currently under redevelopment. We expect to resume registrations during Fall 2023. **

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 285** is an introduction to ordinary differential equations with an emphasis on applications. Topics for this course include first-order, linear higher-order, and systems of differential equations, numerical methods, series solutions, eigenvalues and eigenvectors, Laplace transforms, and Fourier series.

## Math 416: Abstract Linear Algebra

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 416** is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 417: Abstract Algebra

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 417** is an introduction to abstract algebra. The main objects of study are groups, which are abstract mathematical objects that reflect the most basic features of many other mathematical constructions. We will also study rings and fields and other abstract mathematical objects, which can be thought of as groups with additional structure. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 423: Differential Geometry (this course is currently not accepting registrations)

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 423 **this course covers applications of the calculus to the study of the shape and curvature of curves and surfaces; introduction to vector fields, differential forms on Euclidean spaces, and the method of moving frames for low-dimensional differential geometry.

## Math 441: Differential Equations

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 441** is a basic course in ordinary differential equations. Topics include existence and uniqueness of solutions and the general theory of linear differential equations. Treatment is more rigorous than that given in MATH 285. Credit is not given for both MATH 441 and any of MATH 284, MATH 285, and MATH 286. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 442: Intro to Partial Differential Equations

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 442** covers the basic theory of partial differential equations, with a particular emphasize on the wave, diffusion, Laplace and Schrodinger equations. Topics include classification of PDEs in terms of order, linearity and homogeneity, finding the solutions of the PDEs using methods such as geometric, operator, Fourier, separation of variables and spherical means. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 444: Elementary Real Analysis

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 444** is an introduction to ε - δ analysis on real numbers, which makes what the students have learned from calculus courses rigorous. This course is for students who do not plan graduate study (those students should take Math 447). Topics covered by Math 444 include the real number system, limits, continuity, derivatives, the Darboux integral, the Riemann integral, and sequences of functions. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 446: Applied Complex Variables

**Course Description:** This course is available for registration in two different formats: The Academic Year section is available for registration all year round and students have up to 16 weeks to complete the course. The Summer section runs in an 8-week format and is available during the University of Illinois Summer Session II only.

**Math 446** is for students who desire a working knowledge of complex variables; covers the standard topics and gives an introduction to integration by residues, the argument principle, conformal maps, and potential fields. Students desiring a systematic development of the foundations of the subject should take MATH 448. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 447: Real Variables

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 447** is a course on careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. Topics include completeness property of the real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration. Credit is not given for both MATH 447 and either MATH 424 or MATH 444.

## Math 448: Complex Variables (this course is currently not accepting registrations)

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 448** is for students who desire a rigorous introduction to the theory of functions of a complex variable. Topics include Cauchy's theorem, the residue theorem, the maximum modulus theorem, Laurent series, the fundamental theorem of algebra, and the argument principle. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 453: Number Theory

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 453** is a basic introduction to the theory of numbers. Core topics include divisibility, primes and factorization, congruences, arithmetic functions, quadratic residues and quadratic reciprocity, primitive roots and orders. Additional topics covered include sums of squares, Diophantine equations, and continued fractions. This course satisfies the General Education Criteria for Quantitative Reasoning II. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 481: Vector and Tensor Analysis

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 481** is an introductory course in modern differential geometry focusing on examples, broadly aimed at students in mathematics, the sciences, and engineering. Emphasis on rigorously presented concepts, tools and ideas rather than on proofs. The topics covered include differentiable manifolds, tangent spaces and orientability; vector and tensor fields; differential forms; integration on manifolds and Generalized Stokes Theorem; Riemannian metrics, Riemannian connections and geodesics. Applications to configuration and phase spaces, Maxwell equations and relativity theory will be discussed. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload it to Moodle.

## Math 490: Mathematics of Machine Learning

**Course Description:** This course is available for registration all year round and students have up to 16 weeks to complete the coursework.

**Math 490** Machine learning is a growing field at the intersection of probability, statistics, optimization, and computer science, which aims to develop algorithms for making predictions based on data. This course will cover foundational models and mathematics for machine learning, including statistical learning theory and neural networks with a project component. This course uses the Moodle online system. Students must be able to print out assignments, write out solutions, then scan their written work and upload them to Moodle. Students will use Python both within the lessons and to complete two midterm projects and will need to download and use Anaconda software to their computer.