## CME 10: How to learn Mathematics - New ideas from the science of learning (EDUC 105)

This course will help provide the transition from high school to college learning and encourage the positive ideas and mindsets that shape productive learning. We willnconsider what learning theories have to tell us about mathematics learning, the nature of good teaching and the reasons for ongoing inequities in mathematics learning and participation. This seminar is for those who would like a more positive relationship with mathematics, and are interested in learning about ways to tackle education inequalities. Learning goals: First, it introduces students to theories of learning and in particular the learning of mathematics. Mathematics plays a key role in many students¿ learning identities and is often the cause of low self-esteem and anxiety. Research tells us that this is because mathematics in the US is taught in highly ineffective ways. Indeed there is a large gap between what we know works from research and what happens in most mathematics classrooms. This seminar will give participants an understanding of ways to relate positively to mathematics, to learn mathematics most productively and some of the learning barriers that often deny students the opportunity to engage with mathematics in productive ways.nSecond, the course will teach students about the inequalities that pervade the education system in the United States. We will examine the barriers to the participation of women and students of color and we will consider why social class and race are both strong predictors of mathematics achievement. It is hoped that students will leave the course with greater knowledge of why mathematics is important - to themselves and to the future of society.nCourse participants will be given the opportunity to take part in a mathematics camp, designed to change the pathways of middle school students, similar to this previous camp:
https://www.youcubed.org/solving-math- problem/ and to take part in the work of youcubed.org. if they wish.

Terms: Aut
| Units: 1

Instructors:
Boaler, J. (PI)

## CME 100: Vector Calculus for Engineers (ENGR 154)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green¿s, divergence, and Stokes¿ theorems. Examples and applications drawn from various engineering fields. Prerequisites: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext), or
Math 19-21.

Terms: Aut, Win, Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Osgood, B. (PI)
;
Aboumrad, G. (TA)
;
Ahn, S. (TA)
;
Barnes, L. (TA)
;
Bougdal-Lambert, I. (TA)
;
Brown, E. (TA)
;
Corey, N. (TA)
;
El Assad, A. (TA)
;
Fournier-Bidoz, E. (TA)
;
Harvey, B. (TA)
;
Homma, Y. (TA)
;
Infanger, A. (TA)
;
Krason, M. (TA)
;
Lin, Z. (TA)
;
Mantravadi, S. (TA)
;
Pearson, M. (TA)
;
Sanchez, S. (TA)
;
Skochdopole, N. (TA)
;
Slottje, A. (TA)
;
Suo, X. (TA)
;
Tazhimbetov, N. (TA)
;
Yin, H. (TA)

## CME 100A: Vector Calculus for Engineers, ACE

Students attend
CME100/ENGR154 lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Enrollment by department permission only. Prerequisite: must be enrolled in the regular
CME100-01 or 02. Application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Osgood, B. (PI)
;
Aboumrad, G. (TA)
;
Ahn, S. (TA)
;
Barnes, L. (TA)
;
Bougdal-Lambert, I. (TA)
;
Brown, E. (TA)
;
Corey, N. (TA)
;
El Assad, A. (TA)
;
Fournier-Bidoz, E. (TA)
;
Harvey, B. (TA)
;
Homma, Y. (TA)
;
Infanger, A. (TA)
;
Krason, M. (TA)
;
Lin, Z. (TA)
;
Mantravadi, S. (TA)
;
Pearson, M. (TA)
;
Sanchez, S. (TA)
;
Skochdopole, N. (TA)
;
Slottje, A. (TA)
;
Suo, X. (TA)
;
Tazhimbetov, N. (TA)
;
Yin, H. (TA)

## CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext), or
MATH 19-21. Recommended:
CME100.

Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)
;
Moin, P. (PI)
;
Ahn, S. (TA)
;
Amidi, S. (TA)
;
DePaul, G. (TA)
;
Elhafsi, A. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gallegos Ortega, D. (TA)
;
Infanger, A. (TA)
;
Lachevre, P. (TA)
;
Patel, H. (TA)
;
Wang, R. (TA)
;
Westhoff, P. (TA)
;
Wu, H. (TA)

## CME 102A: Ordinary Differential Equations for Engineers, ACE

Students attend
CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students must be enrolled in the regular section (
CME102) prior to submitting application at:n
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)
;
Moin, P. (PI)

## CME 103: Introduction to Matrix Methods (EE 103)

Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series prediction, tomography, optimal control, and portfolio optimization. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
MATH 51 or
CME 100, and basic knowledge of computing (
CS 106A is more than enough, and can be taken concurrently).
EE103/CME103 and
Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.

Terms: Aut, Spr
| Units: 3-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Boyd, S. (PI)
;
Osgood, B. (PI)
;
Tse, D. (PI)
;
Angeris, G. (TA)
;
Chang, S. (TA)
;
Daniel, J. (TA)
;
Degleris, A. (TA)
;
Go, C. (TA)
;
Harvey, B. (TA)
;
Jani, T. (TA)
;
Jimenez, S. (TA)
;
Kamath, G. (TA)
;
Li, L. (TA)
;
Lin, J. (TA)
;
Nishimura, M. (TA)
;
Patel, N. (TA)
;
Pathak, R. (TA)
;
Prakash, L. (TA)
;
Sholar, J. (TA)
;
Spear, L. (TA)

## CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite:
CME 102/
ENGR 155A.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

## CME 104A: Linear Algebra and Partial Differential Equations for Engineers, ACE

Students attend
CME104/ENGR155B lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students must be enrolled in the regular section (
CME104) prior to submitting application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers

Terms: Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)

## CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.

Terms: Win, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Khayms, V. (PI)
;
Amidi, S. (TA)
;
Chen, G. (TA)
;
Chhor, G. (TA)
;
Chu, C. (TA)
;
Lakshman, V. (TA)
;
Pyron, J. (TA)
;
Sagastuy Brena, J. (TA)
;
Wu, Y. (TA)

## CME 108: Introduction to Scientific Computing (MATH 114)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).

Terms: Win, Sum
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

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