FIGURE 4-1. COURSES APPROVED FOR THE MATHEMATICS & STATISTICS REQUIREMENTS
Course
Title
Mathematics*
MATH 19 (A,W,Sum)
Calculus of a Single Variable (or AP/IB Math Credit or equivalent)
20 (A,W,S), 21 (A,W,S)
MATH 41 (A) and 42 (A,W) Calculus of a Single Variable (accelerated; final offering 2016-17)
CME 100** (A,S)
CME 102 (AWS,Sum)
CME 103 (A)
CME 104 (S)
CME 108 (W, Sum)
CME 192 (A,W,S)***
MATH 51** (A,W,S)
MATH 52 (A,W,S)
MATH 53 (A,W,S)
MATH 61CN, 62CM, 63CM
Vector Calculus for Engineers (same as ENGR 154)
Ordinary Differential Equations for Engineers (same as ENGR 155A)
Introduction to Matrix Methods (same as EE 103)
Linear Algebra and Partial Differential Equations for Engineers (same
as ENGR 155B)
Introduction to Scientific Computing
Introduction to MATLAB (4 weeks; A,W,S)
Linear Algebra & Differential Calculus of Several Variables
Integral Calculus of Several Variables
Ordinary Differential Equations with Linear Algebra
Honors Calculus
CEE 101D/201D (A)
CS 103 (A,W)
ENGR 62 (MS&E 111) (A,S)
MATH 104 (A,W)
MATH 106 (S)
MATH 109 (S)
MATH 113 (A,W,S)
MATH 115 (A)
MATH 120 (A,S)
MATH 121 (W)
MATH 131P (A,W)
Computations in CEE
Mathematical Foundations of Computing
Introduction to Optimization
Applied Matrix Theory
Functions of a Complex Variable
Applied Group Theory
Linear Algebra and Matrix Theory
Functions of a Real Variable
Groups and Rings
Galois Theory
Partial Differential Equations
MS&E 121 (S)
Intro to Stochastic Modeling
or more advanced Mathematics courses via approval of petition to deviate
Statistics & Probability*
CME 106 (W, Sum)
Intro to Probability & Statistics for Engineers (same as ENGR
155C
STATS 60/160 (A,W,S,Sum)
Introduction to Statistical Methods: Precalculus
Units
3, 3, 4
5, 5
5
5
4-5
5
3-4
1
5
5
5
5, 5, 5
3
3-5
4
3
3
3
3
3
3
3
3
4
3-4
5
4-5
3-5
3-5
4
5
4
3-4
STATS 110 (A,Sum)
Statistical Methods in Engineering and the Physical Sciences
STATS 116 (A,S,Sum)
Theory of Probability
CS 109 (W,S)
Introduction to Probability for Computer Scientists
EE 178 (A,S)
Probabilistic Systems Analysis
MS&E 120 (A)
Probabilistic Analysis
MS&E 125 (W)
Introduction to Applied Statistics
CEE 203 (A)
Probabilistic Models in Civil Engineering
or more advanced Statistics courses numbered over 100 via approval of petition to deviate
* Some major programs allow only specific courses or allow/require courses in addition to those listed above;
check your major program sheet footnotes to see what specific courses can be applied toward each major.
** If MATH 51 and CME 100 are both taken, only 8 units of credit will be allowed toward the SoE major
program due to overlapping material.
*** Many majors (e.g. BioE) need MATLAB. CME 192 is a 4-week, 1-unit MATLAB course offered A,W,S
THE MATHEMATICS REQUIREMENT
The mathematics requirements for departmental and School of Engineering majors are
delineated by major in the detailed “Program Requirements” section in this Handbook
(Chapter 6). In general, each program requires a number of specific and elective courses from
the list of approved courses shown in Figure 4-1 on the next page. Courses from one of the
mathematics series are required by most of the engineering programs. All engineering
students should check their particular major program in Chapter 6 to see which mathematics
and statistics courses are recommended or required.
Starting with enrollment for Autumn 2016, Stanford will require incoming students to take a
placement diagnostic exam as a prerequisite to enroll in introductory math courses (MATH
19 through 51). Students who have already taken a math course at Stanford can continue in
the sequence without taking the placement diagnostic. The results of the exam will be
forwarded to freshman advisors. Though the suggested placement is a recommendation only,
it will provide useful feedback as they help the student choose where to enter a Stanford math
sequence:
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CME 100, 102, and 104 or 106 (same as ENGR 154, 155A, 155B, and 155C) are
intended for undergraduates interested in engineering; these courses are
recommended by almost all engineering departments. CME 100 presents
multivariable calculus with engineering applications, and introduces MATLAB,
which is incorporated throughout the CME series and will be useful in many later
engineering and science courses. CME 102 covers ordinary differential
equations, CME 104 covers linear algebra and partial differential equations, and
CME 106 covers probability and statistics for engineering – all with an emphasis
on engineering examples and topics. CME 100 and CME 102 each have singlevariable calculus as a prerequisite; CME 104 has CME 102 as a prerequisite;
CME 106 has prerequisites of CME 100, or of MATH 51 or 52
MATH 19, 20, and 21 present single variable calculus.
MATH 41 and 42 cover the same material as MATH 19/20/21, but do so in two
quarters instead of three, with an emphasis on differential calculus in the first
quarter and integral calculus in the second. These accelerated courses will be
offered for the last time in 2016-17.
MATH 51, 52, and 53* may be taken by students who have fulfilled the singlevariable calculus requirement. The 50 series covers similar material, but in a
different order than in the CME series and without a focus on engineering
examples and topics. These courses are taught in an integrated fashion, with
differential calculus of several variables and some basic linear algebra being
taught in MATH 51, integral calculus with linear algebra in MATH 52, and
differential equations, including matrix methods for solving systems, in MATH
53. MATH 51 and 52 can be replaced by CME 100, although students who take
both MATH 51 and CME 100 will receive only 8 units of credit toward their
major due to duplication of material.
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*Note: The MATH department courses do not include MATLAB, which is important
in many engineering fundamental and upper-division engineering courses. To get
MATLAB experience, take the 1-unit CME 192 (4-week course offered A, W, S).