## For Engineers

Chapter 3: The Frosh Canon,

or "So What Courses Are You Taking?"

3.2: Math Options for Engineers

*by USG Academics Committee, last updated 07/31/2016 by Arlene Gamio Cuervo*Most people take two semesters (or the AP equivalent) of single-variable calculus [103 & 104], a term of multivariable calculus [201 or 203], and a term of linear algebra [202 or 204]. A few engineers choose to take the honors sequence [MAT 215, MAT 217, and MAT 218], though it is more geared toward future math majors with an emphasis on proofs rather than applications.

Most introductory math classes meet for one-hour classes on Monday, Wednesday, and Friday, with a single instructor.

The infamous “Calc I”. Students with little or no background in calculus are initially placed in 103. The course covers "basic concepts, methods, and applications of differential and integral calculus of elementary functions of one variable." Many AB students who have already had calculus in high school take this course to fulfill a QR. This makes the curve a little rough. If you had some calculus in high school but aren't sure whether you want to take MAT 103 or go on to MAT 104, we suggest you start out in MAT 104 and only drop down if you're really lost.

This is the continuation of MAT 103, covering integration in further depth along with infinite sequences and series, Taylor expansions, complex algebra, diff-eqs, and applications. To qualify for initial placement into 104, an entering student should score either a 3 or better on the AB Advanced Placement Examination, or should have completed a year of high school calculus and scored 650 or better on the SAT math section.

This course covers "vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes' theorem." To qualify for initial placement into 201, an entering student should have a 3 or better on the BC Calculus AP Exam, or instructor permission. Otherwise, the prerequisites are MAT 104 or MAT 217.

This course covers "calculus of vector functions in space, gradients, chain rule, curvilinear coordinates, multiple integrals, Stokes' theorem, and applications," with "emphasis on both theoretical aspects and problem solving." It is recommended for mathematically inclined scientists and engineers, specifically, students interested in physics. This is a very time-consuming course, and not everyone is a fan. Initial placement into 203 requires a 4 on the BC Calculus AP Exam and a 690 on the SAT (mathematics aptitude) test. Otherwise, the prerequisites are MAT 104 or MAT 217.

Companion course to MAT 201. This course covers "Euclidean spaces, vector spaces, systems of linear equations, matrices and linear transformations, determinants, eigenvalues and applications to systems of differential equations, symmetric matrices, quadratic forms, differentiable vector functions, the chain rule, inverse and implicit functions, and maxima and minima." The prerequisite course is MAT 104 / BC Calculus or instructor permission.

Companion course to MAT 203. This course covers "vector spaces, linear transformations, matrices, determinants and systems of linear equations, eigenvalues, inner product spaces, symmetric matrices, and quadratic forms," along with "applications to calculus in n-dimensional space and systems of differential equations." It’s a more mathematical version of 202, where 203 is a more mathematical version of 201.

This is the intro course to the math major. It does not count as an engineering prerequisite, but some engineers take it anyway. It teaches mathematical proof-writing, gives some basic concepts in set theory, algebra and topology, and covers the material in 103 and 104 with mathematical rigor. This is not a course for the faint of heart.

Companion course to 215, covers basic concepts in abstract algebra and goes over the material in 202 (Linear Algebra) with mathematical rigor: vector spaces, Cayley-Hamilton, Spectral Theorem, etc. This course will fulfill your linear algebra requirement.

This is a yearlong math sequence for International Math Olympiad medalists and other assorted geniuses. It’s meant for math majors, but it’s included here because it actually fulfills the engineering math requirement. This sequence has been taught by charismatic Professor Gunning for some 50 years now, and it’s still kickin’. It crams three rigorous math courses into two semesters: Single and Multivariate Analysis as well as Linear Algebra and other mathematical oddities. Expect jokes about students of French literature.

Most introductory math classes meet for one-hour classes on Monday, Wednesday, and Friday, with a single instructor.

**MAT 103 -- Calculus I**The infamous “Calc I”. Students with little or no background in calculus are initially placed in 103. The course covers "basic concepts, methods, and applications of differential and integral calculus of elementary functions of one variable." Many AB students who have already had calculus in high school take this course to fulfill a QR. This makes the curve a little rough. If you had some calculus in high school but aren't sure whether you want to take MAT 103 or go on to MAT 104, we suggest you start out in MAT 104 and only drop down if you're really lost.

**MAT 104 -- Calculus II**This is the continuation of MAT 103, covering integration in further depth along with infinite sequences and series, Taylor expansions, complex algebra, diff-eqs, and applications. To qualify for initial placement into 104, an entering student should score either a 3 or better on the AB Advanced Placement Examination, or should have completed a year of high school calculus and scored 650 or better on the SAT math section.

**MAT 201 – Multivariable Calculus**This course covers "vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields and Stokes' theorem." To qualify for initial placement into 201, an entering student should have a 3 or better on the BC Calculus AP Exam, or instructor permission. Otherwise, the prerequisites are MAT 104 or MAT 217.

**MAT 203 – Advanced Multivariable Calculus**This course covers "calculus of vector functions in space, gradients, chain rule, curvilinear coordinates, multiple integrals, Stokes' theorem, and applications," with "emphasis on both theoretical aspects and problem solving." It is recommended for mathematically inclined scientists and engineers, specifically, students interested in physics. This is a very time-consuming course, and not everyone is a fan. Initial placement into 203 requires a 4 on the BC Calculus AP Exam and a 690 on the SAT (mathematics aptitude) test. Otherwise, the prerequisites are MAT 104 or MAT 217.

**MAT 202 – Linear Algebra**Companion course to MAT 201. This course covers "Euclidean spaces, vector spaces, systems of linear equations, matrices and linear transformations, determinants, eigenvalues and applications to systems of differential equations, symmetric matrices, quadratic forms, differentiable vector functions, the chain rule, inverse and implicit functions, and maxima and minima." The prerequisite course is MAT 104 / BC Calculus or instructor permission.

**MAT 204 – Advanced Linear Algebra**Companion course to MAT 203. This course covers "vector spaces, linear transformations, matrices, determinants and systems of linear equations, eigenvalues, inner product spaces, symmetric matrices, and quadratic forms," along with "applications to calculus in n-dimensional space and systems of differential equations." It’s a more mathematical version of 202, where 203 is a more mathematical version of 201.

**MAT 215 - Single-Variable Analysis**This is the intro course to the math major. It does not count as an engineering prerequisite, but some engineers take it anyway. It teaches mathematical proof-writing, gives some basic concepts in set theory, algebra and topology, and covers the material in 103 and 104 with mathematical rigor. This is not a course for the faint of heart.

**MAT 217 - Honors Linear Algebra**Companion course to 215, covers basic concepts in abstract algebra and goes over the material in 202 (Linear Algebra) with mathematical rigor: vector spaces, Cayley-Hamilton, Spectral Theorem, etc. This course will fulfill your linear algebra requirement.

**MAT 216-218 - Accelerated Honors Sequence**This is a yearlong math sequence for International Math Olympiad medalists and other assorted geniuses. It’s meant for math majors, but it’s included here because it actually fulfills the engineering math requirement. This sequence has been taught by charismatic Professor Gunning for some 50 years now, and it’s still kickin’. It crams three rigorous math courses into two semesters: Single and Multivariate Analysis as well as Linear Algebra and other mathematical oddities. Expect jokes about students of French literature.