Linear Algebra Course Outline
Shane Rouse
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).
To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems. This material is presented in the first few lectures of 18.02 Multivariable Calculus, and again here.
Martina Balagovic grew up in Zagreb, Croatia. She got her undergraduate degree from the University of Zagreb. She was a graduate student at MIT from 2007, earning a Ph.D. degree in 2011. She is currently a postdoc at the University of York in the UK. She is fascinated by algebra and does research in representation theory.
Linan Chen comes from Shenyang, a city in the northeast of China. After completing her B.A. in Mathematics from Tsinghua University, she continued her graduate study at MIT where she obtained her Ph.D. in Mathematics in 2011. Linan has been an instructor for various math courses, and for her teaching effort, she was awarded the Charles and Holly Housman Award for Excellence in Teaching from the Department of Mathematics at MIT in 2011. Linan also created six recitation sessions for this course in Mandarin Chinese. You can find them in the following sessions:
Benjamin Harris is currently a postdoctoral researcher at Louisiana State University. He obtained his Ph.D. in Mathematics from MIT in 2011. His research concerns Lie groups and their representations. More specifically, he is interested in wave front cycles of tempered representations, Fourier transforms of nilpotent coadjoint orbits, irreducible characters, and branching laws for discrete series.
David Shirokoff grew up in Welland (ON) Canada and completed his undergrad at the University of Toronto. He recently finished his Ph.D. at MIT in applied math under the supervision of Ruben Rosales. His research interests are in applied differential equations, dynamical systems and numerical methods.
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This course provides an accelerated student-driven path through pre-algebra to intermediate algebra. Students will learn the topics in this course at their own pace in a computer lab with faculty guidance. As students demonstrate proficiency, they will have the opportunity to earn credit for Math 85, Math 31, or Math 20. This course has multiple exit levels where students can earn a grade of "P" for passing the highest-level course mastered and become eligible to enter subsequent courses in their plan of study.
Intensive preparation for calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. Topics include algebraic, exponential, logarithmic and trigonometric functions and their inverses and identities, conic sections, sequences, series, the binomial theorem, and mathematical induction.
A review of the core prerequisite skills, competencies, and concepts needed in precalculus. Intended for students who are concurrently enrolled in Math 2, Precalculus. Topics include concepts from elementary algebra, geometry, and intermediate algebra that are needed to understand the basics of college-level precalculus. Emphasis is placed on real and complex numbers; fundamental operations on algebraic expressions and functions; algebraic factoring and simplification; introduction to functions, equations and graphs; circles and parabolas; properties of geometric figures, similarity, and special right triangles. Pass/No Pass only.
This course is intended for students majoring in Science, Technology, Engineering, or Mathematics (STEM). Math 3 in combination with Math 4 (College Algebra for STEM Majors) serves as a prerequisite for Math 7 (Calculus 1). The course includes a study of the properties and graphs of trigonometric and inverse trigonometric functions, trigonometric identities, solutions of triangles, trigonometric equations, parametric equations, polar coordinates and polar equations, the algebra of vectors in two and three dimensions and topics from analytic geometry and applications.
A review of the core prerequisite skills, competencies, and concepts needed in trigonometry. Intended for students who are concurrently enrolled in Math 3, Trigonometry with Applications. Topics include concepts from elementary and intermediate algebra and analytic geometry that are needed to understand the basics of trigonometry. Emphasis is placed on studying angles and their properties; geometric figures including circles and triangles; factoring and simplifying algebraic expressions; equations and graphs of circles; introduction to functions; fundamental operations on algebraic expressions and functions.
This course is intended for students majoring in Science, Technology, Engineering, or Mathematics (STEM). Math 4 in combination with Math 3 (Trigonometry with applications) serves as a prerequisite for Math 7 (Calculus 1). The topics to be covered include review of the fundamentals of algebra, relations, functions, solutions of first and second degree equations and inequalities, systems of equations, matrices, binomial theorem, mathematical induction, polynomial and rational functions, exponential and logarithmic functions, analytic geometry and conic sections, and geometric and arithmetic sequences and series.
A review of the core prerequisite skills, competencies, and concepts needed in College Algebra. Intended for students who are concurrently enrolled in Math 4, College Algebra for STEM Majors. Topics include concepts from elementary and intermediate algebra and analytic geometry that are needed to understand the basics of college-level algebra. Emphasis is placed on real and complex numbers; fundamental operations on algebraic expressions and functions; factoring and simplifying algebraic expressions; introduction to functions, solving equations and systems of linear equations; graphs of elementary functions and their properties.
This first course in calculus is intended primarily for science, technology, engineering, mathematics majors. Topics include limits, continuity, and derivatives and integrals of algebraic and trigonometric functions, with mathematical and physical applications.
This second course in calculus is intended primarily for science, technology, engineering, and mathematics majors. Topics include derivatives and integrals of transcendental functions with mathematical and physical applications, indeterminate forms and improper integrals, infinite sequences and series, and curves, including conic sections, described by parametric equations and polar coordinates.
This course is intended for computer science, engineering, and mathematics majors. Topics include proof techniques, the cardinality of sets, partial orderings and equivalence relations, symbolic logic and valid arguments, permutations and combinations with repetition, and an introduction to graph theory.
Topics include vectors and analytic geometry in two and three dimensions, vector functions with applications, partial derivatives, extrema, Lagrange Multipliers, multiple integrals with applications, vector fields. Green's Theorem, the Divergence Theorem, and Stokes' Theorem
This course is an introduction to ordinary differential equations. Topics include first order equations, linear equations, reduction of order, a variation of parameters, spring motion and other applications, Cauchy-Euler equations, power series solutions, Laplace transforms, and systems of linear differential equations.
Topics include linear, quadratic, exponential and logarithmic functions and equations; systems of linear equations and inequalities; sequences and series. The emphasis is on setting up and solving applications of the algebraic material.
Topics include rational, irrational and complex numbers; fundamental operations on algebraic expressions and functions; introduction to polynomial, rational, exponential and logarithmic functions, equations and graphs; circles and parabolas; matrix row reduction. Emphasis is on advanced algebraic factoring and simplification.
This is a terminal mathematics course for liberal arts and social science majors. Topics include sets and counting, probability, linear systems, linear programming, statistics, and mathematics of finance, with emphasis on applications.
This course provides a review of the core prerequisite skills, competencies, and concepts needed for students who are concurrently enrolled in Finite Mathematics. Topics include theory, procedures, and practices from pre-algebra, beginning algebra, and intermediate algebra. Particular attention is paid to solving and graphing linear equations and inequalities, problem-solving and modeling strategies, translating and interpreting language for the purpose of formulating mathematical phrases and statements, simplifying arithmetic and algebraic expressions, and learning to use the appropriate technology (typically scientific calculators) needed in Math 21. Pass/No Pass only.
This course is a preparatory course for students anticipating enrollment in Math 28 (Calculus I for Business and Social Science). It is not recommended as a terminal course to satisfy transfer requirements. Topics include algebraic, exponential and logarithmic functions and their graphical representations, and using these functions to model applications in business and social science.
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