Pure Mathematics Track

Most mathematics majors complete the pure track. The pure track:

• prepares you for graduate school in mathematics (even if you plan to pursue graduate studies in Applied or Computational Mathematics)
• provides flexibility for students applying mathematics to other disciplines or to niches in business, industry, or government

To complete the recommended four-year Mathematics program, aim to complete the pre-major courses no later than winter quarter of your sophomore year.

Pure Track Pre-Major Requirements

• 20A-B or 19A-B “Calculus”
• 21 “Linear Algebra”
• 23A-B “Multivariable Calculus”

Pure Track Requirements

• 100 “Introduction to Proof & Problem Solving”
• 103 “Complex Analysis”
• 105A “Real Analysis”
• 111A  “Algebra”
• 121A “Differential Geometry” or 124 “Topology” or 128A “Classical Geometry”
• 194 or 195 “Senior Seminar” or “Senior Thesis”
• Three more upper-division mathematics courses numbered 24 or higher (excluding course 88)

Pure Track Recommended Courses

• 24  “Ordinary Differential Equations”
• 30  “Introduction to Problem Solving”
• 105B “Real Analysis”
• 106 “Systems of Ordinary Differential Equations”
• 107 “Partial Differential Equations”
• 110 “Introduction to Number Theory”
• 111B “Algebra”
• 117 “Advanced Linear Algebra”
• 121A “Differential Geometry”
• 124 "Topology"
• 134 "Cryptography"
• 145/L "Chaos Theory" (with lab)

The five pre-major courses and nine required major courses constitute the minimum course load for students planning on applying to graduate school. We encourage you to take as many Mathematics courses as possible and specifically urge you to complete the analysis sequence with courses 105B and the algebra sequence with 111B. We also invite you to enroll in graduate courses, provided you meet the course prerequisites and have the necessary background. If you are unclear about whether you should take a particular course, especially a graduate course, contact the course instructor before the quarter begins.

Pure track sample four-year program

The following program is only a suggestion. It more than satisfies the minimum requirements for a degree in pure Mathematics and is suitable preparation for any student interested in going on to graduate school. Using it as a framework, develop your own schedule choosing electives that interest you, and discuss it with your advisor. Courses marked with an asterisk (*) are required courses, and the courses marked with an asterisk in parentheses means the requirement can be met by more than one course, others are recommended electives. (At least three upper-division electives are required to fulfill the minimum number of courses.)

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