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Sample Course Plans

Students majoring in mathematics have a wide range of eventual interests: some go into academia, a finance, cryptography, the tech industry, and more.

The sample course plans below are examples of course selections a Math major can take depending on their interests. These sample plans are simply possibilities; there are many choices a Math major can make based on their interests.

Note: Math 56 (Proofs and Modern Mathematics, 4 units) can be used as part of any of the sample plans provided below in place of any of the listed Math department courses or electives.

Applied Math

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM 
  • Math 61DM, Math 62DM, Math 63DM

Eight of the following Math Courses:

  • Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (4 units)
  • Math 107: Graph Theory (4 units)
  • Math 108: Introduction to Combinatorics and its Applications (4 units)
  • Math 109: Applied Group Theory or Math 120: Groups and Rings (4 units)
  • Math 110: Applied Number Theory and Field Theory (4 units)
  • Math 115: Functions of a Real Variable or Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 144: Introduction to Geometry and Topology (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 173: Theory of Partial Differential Equations (4 units)
  • Math 175: Elementary Functional Analysis (4 units)

4 additional elective courses from Computer Science, Economics, Engineering, Physics, and Statistics 

Artificial Intelligence & Machine Learning

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM
  • Math 61DM, Math 62DM, Math 63DM

Math Courses:

  • Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 108: Introduction to Combinatorics and Its Applications (4 units)
  • Math 115: Functions of a Real Variable (4 units)
  • Math 136: Stochastic Processes (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 158: Probability and Stochastic Differential Equations for Applications (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 175: Elementary Functional Analysis (4 units)

Four of the following elective courses:

  • CS 161: Design and Analysis of Algorithms (5 units)
  • CS 221: Artificial Intelligence: Principles and Techniques (4 units)
  • CS 224N: Natural Language Processing with Deep Learning (4 units)
  • CS 228: Probabilistic Graphical Models: Principles and Techniques (4 units)
  • CS 229: Machine Learning (4 units) or CS 229M: Machine Learning Theory (3 units)
  • EE 364A: Convex Optimization I (3 units)
  • STATS 200: Introduction to Statistical Inference (4 units)
Computer Graphics/Numerical Methods

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM
  • Math 61DM, Math 62DM, Math 63DM

Math Courses:

  • Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 143: Differential Geometry (4 units)
  • Math 144: Introduction to Geometry and Topology (4 units)
  • Math 147: Differential Topology or Math 148: Algebraic Topology (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 172: Lebesgue Integration and Fourier Analysis or Math 205A: Real Analysis (3-4 units)
  • Math 175: Elementary Functional Analysis or Math 205B: Real Analysis (4 units)

Four of the following as electives:

  • CS 148: Introduction to Computer Graphics and Imaging (4 units)
  • CS 205L: Continuous Mathematical Methods with an Emphasis on Machine Learning (3 units)
  • CME 302: Numerical Linear Algebra* (3 units)
  • Math 226/CME 306: Numerical Solution of Partial Differential Equations (3 units)
  • Math 228/CME308/MS&E 324: Stochastic Methods in Engineering (3 units)
  • EE 261: The Fourier Transform and its Applications (3 units)

*Sufficient to have taken Math 113; know basic coding.

Courses that are less essential to Computer Graphics/Numerical Methods but are useful:

  • Math 107: Graph Theory (4 units)
  • Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (4 units)
  • Math 120: Groups and Rings (4 units)
  • Math 220/CME 303: Partial Differential Equations of Applied Mathematics (3 units)
  • Physics 61: Mechanics and Special Relativity (4 units)
  • Physics 110: Advanced Mechanics (4 units)
Computational Neuroscience

One of the following (10 units):

  • Math 19, Math 20, Math 21 or AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 or 
  • Math 61DM, Math 62DM, Math 63DM

Eight of the following Math courses:

  • Math 56: Proofs and Modern Mathematics (4 units)
  • Math 104: Applied Matrix Theory (4 units) or Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 106: Functions of a Complex Variable (4 units) or Math 116: Complex Analysis (4 units)This course is strongly recommended (for applications of contour integration in Fourier analysis). 
  • Math 115: Functions of a Real Variable (4 units) or Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 118: Mathematics of Computation (4 units)
  • Math 131P: Partial Differential Equations (4 units) or Math 173: Theory of Partial Differential Equations (4 units)
  • Math 136: Stochastic Processes (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 159: Discrete Probabilistic Methods (4 units)
  • Math 220B: Computational Methods of Applied Mathematics (3 units)
  • Math 228: Stochastic Methods in Engineering (3 units)

Four of the following as electives:

  • Applied Physics 229: Statistical Mechanics of Learning and Computation (3 units)
  • Applied Physics 293: Theoretical Neuroscience (3 units)
  • EE 102A: Signals and Systems I (4 units)
  • EE 261: The Fourier Transform and Its Applications (3 units)
  • EE 269: Signal Processing for Machine Learning (3 units)
  • CS 230: Deep Learning (3-4 units)
Cryptography

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61DM, Math 62DM, Math 63DM

Eight of the following Math courses:

  • Math 107: Graph Theory (4 units)
  • Math 110: Number Theory for Cryptography (4 units)
  • Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 120: Groups and Rings (4 units)
  • Math 121: Galois Theory (4 units)
  • Math 145: Algebraic Geometry (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 154: Algebraic Number Theory (4 units)
  • Math 159: Discrete Probabilistic Methods (4 units)

4 additional elective courses from Computer Science and Statistics 

Data Science

One of the following (10 units):

  • Math 19, Math 20, Math 21
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53
  • Math 61CM, Math 62CM, Math 63CM 
  • Math 61DM, Math 62DM, Math 63DM

Math Courses:

  • Math 104: Applied Matrix Theory (4 units)
  • Math 107: Graph Theory (4 units)
  • Math 108: Introduction to Combinatorics and its Applications (4 units)
  • Math 115: Functions of a Real Variable (4 units)
  • Math 136: Stochastic Processes (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 158: Probability and Stochastic Differential Equations for Applications (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)

Elective courses from Computer Science and Statistics (4 courses).

  • Stats 200 (4 units)
  • Stats 191 or 203 (3 units)
  • Stats 202 or 216 (3 units)
  • MS&E 111 (4 units)
Evolution & Ecology

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53
  • Math 61CM, Math 62CM, Math 63CM
  • Math 61DM, Math 62DM, Math 63DM

Eight of the following Math courses:

  • Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 108: Introduction to Combinatorics and its Applications (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 115: Functions of a Real Variable (4 units)
  • Math 131P: Partial Differential Equations (4 units)
  • Math 136: Stochastic Processes or Math 158: Basic Probability and Stochastic Processes with Engineering Applications (4 units)
  • Math 159: Discrete Probabilistic Methods (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 173: Theory of Partial Differential Equations (4 units)

Four of the following elective courses:

  • Bio 113: Fundamentals of Molecular Evolution (4 units)
  • Bio 172:  Ecological Dynamics: Theory and Applications (4 units)
  • Bio 183: Theoretical Population Genetics (3 units)
  • CS 161: Design and Analysis of Algorithms (5 units)
  • Stats 155: Statistical Methods in Computational Genetics (3 units)
Finance

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM

Math Courses:

  • Math 104: Applied Matrix Theory (4 units)
  • Math 115: Functions of a Real Variable (4 units)
  • Math 136: Stochastic Processes (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 131P: Partial Differential Equations (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 173: Theory of Partial Differential Equations (4 units)
  • Math 175: Elementary Functional Analysis (4 units)

Four of the following elective courses:

  • Math 230A/Stats 310A: Theory of Probability (3 units)
  • Math 236: Introduction to Stochastic Differential Equations (3 units)
  • Math 237: Default and Systemic Risk (3 units)
  • Math 238/Stats 250: Mathematical Finance (3 units)
  • MS&E 245A: Investment Science* (4 units)
  • MS&E 245B: Advanced Investment Science** (3 units)
  • Stats 200: Introduction to Statistical Inference (4 units)
  • Stats 305A: Applied Statistics I (3 units)

* Provides a first introduction to financial math. Sufficient background for this course is provided by Math 104, Math 136, and Stats 118.

** Gives additional undergraduate-level instruction in financial math. Math 131P is helpful background.

Physics

One of the following (10 units):

  • Math 19, Math 20, Math 21 
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM

Eight of the following courses:

  • Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (4 units)
  • Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 115: Functions of a Real Variable or Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 120: Groups and Rings (4 units)
  • Math 122: Modules and Group Representations (4 units)
  • Math 131P: Partial Differential Equations or Math 173: Theory of Partial Differential Equations (4 units)
  • Math 143: Differential Geometry (4 units)
  • Math 144: Introduction to Geometry and Topology (4 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 175: Elementary Functional Analysis (4 units)

4 additional elective courses from Physics, Engineering, and Statistics.

Pure & Applied Interests

One of the following (10 units):

  • Math 19, Math 20, Math 21  
  • AP Calculus

One of the following sequences (15 units):

  • Math 51, Math 52, Math 53 
  • Math 61CM, Math 62CM, Math 63CM 
  • Math 61DM, Math 62DM, Math 63DM

Math Courses:

  • Math 104: Applied Matrix Theory or Math 113: Linear Algebra and Matrix Theory (4 units)
  • Math 106: Functions of a Complex Variable or Math 116: Complex Analysis (4 units)
  • Math 109: Applied Group Theory or Math 120: Groups and Rings (4 units)
  • Math 110: Applied Number Theory and Field Theory or Math 121: Galois Theory (4 units)
  • Math 115: Functions of a Real Variable (4 units)

Eight of the following courses including at least three Math courses:

  • Math 107: Graph Theory (4 units)
  • Math 108: Introduction to Combinatorics and its Applications (4 units)
  • Math 143: Differential Geometry (4 units)
  • Math 144: Introduction to Geometry and Topology (4 units)
  • Math 147: Differential Topology (4 units) 
  • Math 148: Algebraic Topology (4 units)
  • Math 152: Elementary Theory of Numbers (4 units)
  • Math 161: Set Theory (4 units)
  • Math 171: Fundamental Concepts of Analysis (4 units)
  • Math 173: Theory of Partial Differential Equations (4 units)
  • Econ 50: Economic Analysis I (5 units)
  • Physics 41: Mechanics (3 units)
  • Physics 43: Electricity and Magnetism (3 units)
  • Physics 45: Light and Heat (3 units)
  • Math 151: Introduction to Probability Theory (4 units) or Stats 118: Theory of Probability II (4 units)