ucsb · BS

Applied Mathematics

UC Santa Barbara

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MATH 3A

4 units

Calculus with Applications, First Course

Differential calculus including analytic geometry, limits, derivatives, techniques and applications of differentiation; introduction to integration; logarithmic and trigonometric functions.

MATH 4A

4 units

Linear Algebra with Applications

Systems of linear equations, matrix algebra, determinants, vector spaces and subspaces, basis and dimension, linear transformations, eigenvalues and eigenvectors, diagonalization, and orthogonality.

MATH 8

5 units

Transition to Higher Mathematics

Propositional logic, techniques of mathematical proof, and fundamental structures including sets, functions, and relations. Essential preparation for upper-division mathematics major courses.

PHYS 7A

4 units

Basic Physics

Kinematics in 3D, Newton's laws, energy, momentum and collisions, rotation, statics and equilibrium.

MATH 118A

4 units

Real Analysis

Axioms of the real numbers, topology of metric spaces, numerical sequences, and infinite series.

MATH 111A

4 units

Abstract Algebra

Introduction to group theory for finite groups: homomorphisms, normal subgroups, quotients, direct products, group actions, and classification of finitely generated Abelian groups.

MATH 124

4 units

Partial Differential Equations

Wave, heat, and potential equations. (UCSB catalog: MATH 124A.)

MATH 132

4 units

Optimization

Global and local optimization, constrained and unconstrained optimization, convex versus nonconvex optimization, gradient methods, Newton and quasi-Newton methods, and trust region methods. (UCSB catalog: MATH 132A.)

MATH 160

4 units

Introduction to Numerical Analysis

Numerical methods for nonlinear equations (Newton method), integration (quadrature and composite integration), and initial value problems for ODEs (Euler and Runge–Kutta methods). (UCSB catalog: MATH 104A.)

MATH 170

4 units

Introduction to Mathematical Finance

Mathematical methods for asset pricing models, equilibrium and derivative pricing, options, bonds, and the term structure of interest rates; optimization models for risk management and financial engineering.

CareerData science

Data science

Entry $78K–$125K/yr

Career path for Applied Mathematics graduates: data science.

CareerEngineering

Engineering

Entry $60K–$94K/yr

Career path for Applied Mathematics graduates: engineering.

CareerFinance

Finance

Entry $55K–$85K/yr

Career path for Applied Mathematics graduates: finance.

CareerResearch

Research

Entry $40K–$62K/yr

Career path for Applied Mathematics graduates: research.

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Critical path

MATH 3A -> MATH 4A -> MATH 8 -> PHYS 7A -> MATH 118A -> MATH 111A -> MATH 124 -> MATH 132 -> MATH 160 -> MATH 170

Top bottlenecks

MATH 3A unlocks 9 downstream courses.
MATH 4A unlocks 8 downstream courses.
MATH 8 unlocks 7 downstream courses.

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