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MATH 121A: Mathematical Tools for the Physical Sciences
4.00 Credits
University of California-Berkeley
Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Rapid review of series and partial differentiation, complex variables and analytic functions, integral transforms, calculus of variations.
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MATH 121A - Mathematical Tools for the Physical Sciences
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MATH 123: Ordinary Differential Equations
4.00 Credits
University of California-Berkeley
Existence and uniqueness of solutions, linear systems, regular singular points. Other topics selected from analytic systems, autonomous systems, Sturm-Liouville Theory.
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MATH 123 - Ordinary Differential Equations
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MATH 125A: Mathematical Logic
4.00 Credits
University of California-Berkeley
Sentential and quantificational logic. Formal grammar, semantical interpretation, formal deduction, and their interrelation. Applications to formalized mathematical theories. Selected topics from model theory or proof theory.
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MATH 125A - Mathematical Logic
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MATH 126: Introduction to Partial Differential Equations
4.00 Credits
University of California-Berkeley
Waves and diffusion, initial value problems for hyperbolic and parabolic equations, boundary value problems for elliptic equations, Green's functions, maximum principles, a priori bounds, Fourier transform.
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MATH 126 - Introduction to Partial Differential Equations
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MATH 128A: Numerical Analysis
4.00 Credits
University of California-Berkeley
Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.
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MATH 128A - Numerical Analysis
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MATH 135: Introduction to the Theory of Sets
4.00 Credits
University of California-Berkeley
Set-theoretical paradoxes and means of avoiding them. Sets, relations, functions, order and well-order. Proof by transfinite induction and definitions by transfinite recursion. Cardinal and ordinal numbers and their arithmetic. Construction of the real numbers. Axiom of choice and its consequences.
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MATH 135 - Introduction to the Theory of Sets
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MATH 142: Elementary Algebraic Topology
4.00 Credits
University of California-Berkeley
The topology of one and two dimensional spaces: manifolds and triangulation, classification of surfaces, Euler characteristic, fundamental groups, plus further topics at the discretion of the instructor.
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MATH 142 - Elementary Algebraic Topology
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MATH 143: Elementary Algebraic Geometry
4.00 Credits
University of California-Berkeley
Introduction to basic commutative algebra, algebraic geometry, and computational techniques. Main focus on curves, surfaces and Grassmannian varieties.
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MATH 143 - Elementary Algebraic Geometry
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MATH 152: Mathematics of the Secondary School Curriculum II
4.00 Credits
University of California-Berkeley
Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry.
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MATH 152 - Mathematics of the Secondary School Curriculum II
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MATH 16A: Analytic Geometry and Calculus
3.00 Credits
University of California-Berkeley
This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions.
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MATH 16A - Analytic Geometry and Calculus
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