ucsb · BS

Financial Mathematics and Statistics

UC Santa Barbara

26 nodes24 edgesv1 · approved

ECON 1

4 units

Principles of Microeconomics

Supply, demand, market equilibrium, and consumer choice—pre-major foundation for financial economics.

ECON 2

4 units

Principles of Macroeconomics

National income, inflation, unemployment, and fiscal and monetary policy.

MATH 3A

4 units

Calculus I

Limits, derivatives, and integrals—core preparation for probability, finance, and numerical methods.

MATH 3B

4 units

Calculus II

Advanced integration, sequences, and series for upper-division math and statistics.

MATH 4A

4 units

Linear Algebra

Matrices, vector spaces, and linear systems—essential for statistics and computational finance.

ECON 10A

5 units

Intermediate Microeconomics

Formal microeconomic theory: utility maximization, production, and market structure.

CMPSC 8

4 units

Introduction to Python

Python programming for data analysis—required preparation for quantitative finance coursework.

Self-learnable

MATH 6A

4 units

Vector Calculus I

Multivariable calculus and partial derivatives for advanced math and modeling courses.

PSTAT 10

5 units

Probability and Statistics

Introductory probability and statistics; gateway to the FMS upper-division core.

MATH 4B

4 units

Differential Equations

Ordinary differential equations with applications in economics and mathematical modeling.

MATH 8

5 units

Transition to Proofs

Proof techniques and discrete mathematics; prerequisite for MATH 117 and PSTAT 120A.

MATH 6B

4 units

Vector Calculus II

Vector calculus theorems and applications in physics, engineering, and applied math.

PSTAT 120A

4 units

Probability

Rigorous probability theory for statistics, finance, and stochastic modeling.

PSTAT 120B

4 units

Statistics

Statistical inference, estimation, and hypothesis testing methods.

PSTAT 160A

4 units

Mathematical Statistics

Theoretical statistics: sufficiency, estimation theory, and statistical decision making.

PSTAT 160B

4 units

Mathematical Statistics II

Advanced topics in statistical theory and inference for graduate-level preparation.

PSTAT 126

4 units

Regression Analysis

Linear regression, model selection, and applied predictive analytics.

MATH 117

4 units

Series and Sequences

Convergence, power series, and Fourier series—prep for numerical analysis sequence.

MATH 104A

4 units

Numerical Analysis

Numerical methods for root-finding, interpolation, and solving linear systems.

PSTAT 170

4 units

Mathematical Finance

Derivatives pricing, portfolio optimization, and stochastic models in finance.

MATH 104B

4 units

Numerical Analysis II

Numerical ODE/PDE methods and approximation theory for applied mathematics.

MATH 104C

4 units

Numerical Analysis III

Advanced numerical techniques and computational methods for scientific computing.

CareerQuant Finance

Quantitative Finance / Trading

Entry $85K–$135K/yr

Derivatives, algorithmic trading, and risk modeling at banks, hedge funds, and fintech firms.

CareerRisk Analyst

Risk Management & Insurance

Entry $55K–$85K/yr

Measure and mitigate market, credit, and operational risk for financial institutions.

CareerData Science

Data Science & Analytics

Entry $78K–$125K/yr

Build statistical and ML models for product, marketing, and business analytics teams.

CareerGrad School

MS/PhD in Statistics or Financial Math

Graduate stipend or fellowship — typically $22K–$42K/yr; not full-time W-2 salary.

Research careers in statistics, financial mathematics, or econometrics at top graduate programs.

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Critical path

MATH 3A -> MATH 3B -> MATH 4A -> MATH 8 -> MATH 117 -> MATH 104A -> MATH 104B -> MATH 104C

Top bottlenecks

MATH 3A unlocks 17 downstream courses.
MATH 3B unlocks 15 downstream courses.
MATH 4A unlocks 12 downstream courses.

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