# Undergraduate Courses

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Code | Course Description |
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Math 2 | Mathematics in Everyday Life
This course covers basic mathematical concepts and skills applied to everyday life.
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Prerequisite: None Number of units: 3 Number of hours/week: 3 Additional notes: This is a general education (GE) course. This cannot be taken by students in degree programs requiring a math service course, including Math 20. Math 2 Syllabus |

Math 10 | Mathematics, Culture and Society
Appreciation of the beauty and power of mathematics through the examination of its nature, development and utility, and its relationship with culture and society.
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Prerequisite: None Number of units: 3 Number of hours/week: 3 Additional notes: This is a general education (GE) course. Math 10 is open to all UP students in any degree program. BS Mathematics majors may take the course provided they are in their first year of college. Math 10 Syllabus |

Math 20 | Precalculus: Functions and their Graphs
Equations and inequalities; two dimensional coordinate system, graphs of equations; conic sections; functions and their graphs; trigonometric functions and trigonometric identities; inverse trigonometric functions; solutions of triangles; polar form of complex numbers.
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Prerequisite: High School Algebra/equiv Number of units: No credit Number of hours/week: 4 Additional notes: This course is intended for non-STEM track high school graduates who are admitted to degree programs requiring at least Math 21. It is considered as an audit course and the grade is non-numerical (P for Passed and F for Failed). A Validation Examination for Math 20 may be taken by students (either freshmen or transferees) from non-STEM high school tracks admitted to degree programs requiring Math 21. Those who pass the Validation Exam may enroll in Math 21. Math 20 Syllabus |

Math 21 | Elementary Analysis I
Limits and continuity; derivatives of algebraic and transcendental functions (exponential, logarithmic, trigonometric, hyperbolic, and their inverses); applications of derivatives; antiderivatives and definite integrals; Fundamental Theorem of Calculus; applications of the definite integral.
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Prerequisite: High School Basic Calculus from the STEM or equivalent strand of K-12, or Math 20/equiv Number of units: 4 Number of hours/week: 4 Additional notes: This is a service course and a core course for BS Mathematics students. An Advanced Placement Examination (APE) for Math 21 may be taken by incoming freshmen students who have taken calculus in high school. Those who pass the APE may enroll in Math 22. Math 21 Syllabus |

Math 22 | Elementary Analysis II
Techniques of integration; improper integrals; parametric equations and polar coordinates; lines in space, planes, cylindrical surfaces, surfaces of revolution, and quadric surfaces; vectors and vector-valued functions; sequences and series.
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Prerequisite: Math 21/equiv Number of units: 4 Number of hours/week: 4 Additional notes: This is a service course and a core course for BS Mathematics students. Math 22 Syllabus |

Math 23 | Elementary Analysis III
Functions of several variables; limits and continuity of functions of several variables; partial derivatives and the total differential; directional derivatives; relative and absolute extrema of functions of several variables; double and triple integrals; applications of multiple integrals; vector fields; line and surface integrals.
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Prerequisite: Math 22/equiv Number of units: 4 Number of hours/week: 4 Additional notes: This is a service course and a core course for BS Mathematics, Minor in Mathematical Foundations and Methods, and Diploma in Mathematics students. Math 23 Syllabus |

Math 30 | Intermediate Analysis and Applications
Integration techniques; multivariate calculus; sequences and series; introduction to matrices; applications to economics, business, life and social sciences.
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Prerequisite: Math 21/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a service course. Math 30 Syllabus |

Math 40 | Linear Algebra
Vector spaces; linear transformations; matrices; eigenvalues; canonical forms; orthogonality; applications.
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Prerequisite: Math 22/equiv or Math 30/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a service course and a core course for Minor in Mathematical Foundations and Methods and Diploma in Mathematics students. Math 40 Syllabus |

Math 108 | Foundations of Abstract Mathematics
Propositional and predicate calculus; methods of proof; algebra of sets; relations and functions; finite and infinite sets.
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Prerequisite: Math 21/equiv or COI Number of units: 4 Number of hours/week: 4 Additional notes: This is a core course for BS Mathematics, Minor in Mathematical Foundations and Methods, and Diploma in Mathematics students. Math 108 Syllabus |

Math 110.1 | Abstract Algebra I
Groups, group homomorphism; permutation groups; factor groups; rings, ring homomorphism, ideals, integral domains; introduction to fields, field of quotients.
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Prerequisite: Math 108/equiv or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics and Diploma in Mathematics students. Math 110.1 Syllabus |

Math 110.2 | Abstract Algebra II
Vector spaces; linear transformations; matrices; diagonalizability; eigenvalues and eigenvectors; inner product spaces; normal matrices.
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Prerequisite: Math 110.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 110.2 Syllabus |

Math 110.3 | Abstract Algebra III
Polynomial rings and factorization; field extensions, splitting fields, finite fields, field automorphisms; introduction to Galois theory.
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Prerequisite: Math 110.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 110.3 Syllabus |

Math 117 | Elementary Theory of Numbers
Divisibility, Euclidean algorithm, primes and the fundamental theorem of arithmetic, congruences, systems of linear congruences, primitive roots, primality testing, cryptography, quadratic residues and the quadratic reciprocity law, Diophantine equations.
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Prerequisite: Math 108/equiv or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics and Diploma in Mathematics students. Math 117 Syllabus |

Math 122 | Differential Equations and Applications
First order ordinary differential equations (ODEs); homogeneous and nonhomogeneous linear second order ODEs; systems of linear equations; series solutions of ODEs; stability analysis of nonlinear ODEs; Laplace transforms; applications of ODEs.
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Prerequisite: Math 22/equiv or Math 30/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics, Minor in Mathematical Foundations and Methods, and Diploma in Mathematics students. Math 122 Syllabus |

Math 123.1 | Advanced Calculus I
The real number system; point set topology; sequences of real numbers; limits and continuity; the derivative; the Riemann integral; sequences of functions; uniform convergence.
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Prerequisite: Math 23/equiv and Math 108/equiv, or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics and Diploma in Mathematics students. This can be taken as a math elective for students taking the Minor in Mathematical Foundations and Methods program. Math 123.1 Syllabus |

Math 123.2 | Advanced Calculus II
Series of real numbers; series of functions; power series; topology of \(\mathbb{R}^n\); limits, continuity and differentiability of functions of several variables; implicit and inverse function theorems; multiple integration; improper integrals; transformations.
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Prerequisite: Math 123.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 123.2 Syllabus |

Math 126 | Real Analysis
Properties of real numbers; integral of step functions; Lebesgue integral; convergence theorem; measurable functions; measurable sets.
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Prerequisite: Math 123.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics students. Math 126 Syllabus |

Math 128 | Complex Analysis
Complex numbers and properties; analytic functions and the Cauchy-Riemann equations; power series representation of analytic functions; complex integration; Cauchy integral formula and its consequences; singularities, Laurent series, and residues; applications to definite integrals.
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Prerequisite: Math 123.1/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 128 Syllabus |

Math 131 | Elementary Set Theory
Axioms of Set Theory; relations and functions; natural numbers, cardinal numbers and the Axiom of Choice; orderings and ordinals.
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Prerequisite: Math 110.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics students. |

Math 133 | Introduction to Mathematical Modeling
Overview of mathematical modeling; discrete models; model fitting; linear programming; linear and nonlinear continuous models; numerical methods; optimization of continuous models.
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Prerequisite: CS 11/equiv and Math 122/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. This can be taken as a math elective for students taking the Minor in Mathematical Foundations and Methods program. Math 133 Syllabus |

Math 140 | Introduction to Modern Geometries
Development of modern geometries; finite geometries; geometric transformations; projective geometry; non-Euclidean geometries.
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Prerequisite: Math 108/equiv or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 140 Syllabus |

Math 142 | Elementary Topology
Topological spaces; continuous functions and homeomorphisms; compactness and connectedness; separation axioms.
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Prerequisite: Math 123.1 or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 142 Syllabus |

Math 146 | Introduction to Differential Geometry
Elementary topology; calculus of several variables; curves and surfaces; theorems of Stokes and Gauss; differential forms.
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Prerequisite: Math 23/equiv and Math 140/equiv, or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a geometry elective for BS Mathematics students. Math 146 Syllabus |

Math 147 | Introduction to Algebraic Geometry
Projective varieties; algebraic and elliptic curves.
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Prerequisite: Math 110.1 and Math 140 Number of units: 3 Number of hours/week: 3 Additional notes: This is a geometry elective for BS Mathematics students. Math 147 Syllabus |

Math 148 | Introduction to Projective Geometry
Projective planes and spaces.
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Prerequisite: Math 110.1 and Math 140 Number of units: 3 Number of hours/week: 3 Additional notes: This is a geometry elective for BS Mathematics students. Math 148 Syllabus |

Math 150.1 | Mathematical Statistics I
Combinatorial probability; probability distributions; joint and conditional distributions; random variables; distributions of functions of random variables; mathematical expectation; moment-generating functions; sampling distributions.
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Prerequisite: Math 23/equiv and Stat 101/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics, Minor in Mathematical Foundations and Methods, and Diploma in Mathematics students. Math 150.1 Syllabus |

Math 150.2 | Mathematical Statistics II
Limiting distributions; estimation of parameters; tests of hypotheses; regression and correlation; analysis of variance; applications.
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Prerequisite: Math 150.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics students. Math 150.2 Syllabus |

Math 158 | Introduction to Discrete Mathematics
Permutations and combinations; binomial and multinomial coefficients; the Principle of Inclusion and Exclusion; graphs and their properties; families of graphs, distance and connectivity in graphs, selected topics in discrete mathematics.
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Prerequisite: Math 108/equiv or COI Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics and Minor in Mathematical Foundations and Methods students. Math 158 Syllabus |

Math 162 | Theory of Interest
Simple interest; compound interest; continuous interest; annuities; amortization schedules and sinking funds; bonds and other securities; special topics.
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Prerequisite: Math 22/equiv or Math 30/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics and Minor in Mathematical Foundations and Methods students. Math 162 Syllabus |

Math 164 | Mathematics of Life Contingencies
Mathematical theory of life contingencies involving single-life functions; mortality; life annuities and insurances; reserves; expense factor; population theory.
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Prerequisite: Math 150.1/equiv and Math 162/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics students. Math 164 Syllabus |

Math 166 | Mathematics of Finance
Bond-Stock market; immunization; forwards and futures; options, including binomial pricing and Black-Scholes pricing; greeks of options, swaps; hedging and investment strategies.
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Prerequisite: Math 162 Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics students. Math 166 Syllabus |

Math 171 | Numerical Analysis
Error analysis; solution of a single nonlinear equation; solution of systems of equations; solution of ordinary differential equations; series.
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Prerequisite: Math 122/equiv and Math 110.2/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a core course for BS Mathematics and Diploma in Mathematics students. Math 171 Syllabus |

Math 180.1 | Operations Research I
Introduction to linear programming; the simplex method; duality; sensitivity analysis; integer programming; nonlinear programming.
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Prerequisite: Math 40/equiv Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics and Minor in Mathematical Foundations and Methods students. Math 180.1 Syllabus |

Math 180.2 | Operations Research II
Review of probability theory; Stochastic models; Markov chains; introduction to queueing theory; introduction to simulation; games, replacement and reliability theory.
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Prerequisite: Math 180.1 and Math 150.1 Number of units: 3 Number of hours/week: 3 Additional notes: This is a math elective for BS Mathematics students. |

Math 190 | Introduction to Mathematical Research and Writing
Basic principles and best practices of mathematical research and writing.
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Prerequisite: Junior Standing Number of units: 2 Number of hours/week: 2 Additional notes: This is a core course for BS Mathematics students. Math 190 Syllabus |

Math 197 | Special Topics
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Prerequisite: COI Number of units: 3 Additional notes: This is a math elective for BS Mathematics students. It may be taken at most three times provided topics are different; topics to be specified. |

Math 200 | Undergraduate Thesis
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Prerequisite: Senior Standing Number of units: 3 Additional notes: This is a core course for BS Mathematics students. |