catalogue of courses_mathematics2011

7/29/2019 Catalogue of Courses_mathematics2011

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Republic of the PhilippinesCARAGA STATE UNIVERSITY

P.O. Box 165, Ampayon, Butuan CityCARAGA Administrative Region XIII

Tel. No (085) 3423047 Fax No. (085) 3421079

DEPARTMENT OF MATHEMATICS

SUMMARY OF COURSE OFFERING

A. GENERAL EDUCATION SUBJECTS

Course No. Credit Course Title Prerequisites Course Description

Lec Lab Total

Math 1 3 0 3 Integrative

Course in

Math

CSU SAE Real number System, topics in Geometry,

Measurement; Algebra; Statistics.

Math 1.1 3 0 3 Fundamentals

of Mathematics This is an integrative course. It

involves the review of the real number

systems, Application of Rational Numbersincluding Ratio and Proportion; topics in

Geometry; Measurement; Algebra ( Linear

Equations and Inequalities, QuadraticEquations, Equations involving fractions,

Graphs)

Math 1.2 3 0 3 Intro to

College Math

Sets; The Real Number System; Algebraic

Expressions and Polynomials; Positive

Integral Components and Radicals; PlaneCoordinate System; Equation in One

Variable; Equations in Two Variables.Math 1.3 3 0 3 Advanced

Algebra and

Trigonometry

Math 1.1 Axioms of Order; Radicals: Rational

Exponents: Complex Numbers;Inequalities; Circles and Parabola;

Functions- Exponential, Logarithmic;

Circular Functions; Trigonometric Ratio;Solutions of Right triangles; Sine and

Cosine Law; Identities; Navigation

Problem and other Applications.

Math 1.4 3 0 3 Plane

TrigonometryMath 1.7 Trigonometric functions; solutions of right

Triangles; Analytic Trigonometry-

Trigonometric Identities, Inverse

Trigonometric Functions; Application ofTrigonometry- sine and Cosine Law,

Vectors, Polar coordinates, Polar form of

complex Numbers; Selected Topics inAlgebra- Sequences and Series,

Mathematical Induction, Arithmetic and

Geometric Sequences and Series.

Math 1.5 3 0 3 Mathematical

Investigation

and ModelingProblem Solving and MathematicalInvestigations; Writing/Reporting

Mathematical Investigations; Assessing

Mathematical Investigations; Teachingthrough Mathematical Investigations.


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Math 1.6 2 1 3 Technology in

Math

Graphics Calculators; Geometry Software;

Computer Algebra Systems; Presentation

Software; Spreadsheet Solution; Internet andJava Applets; Web

Math 1.7 3 0 3 College

Algebra

CSUSAE Sets; Real Number Systems; Polynomials

and Rational Expressions; RationalExponents and Radicals; Equations in One

Variable; Inequalities; Algebraic

Functions; Exponential and Logarithmic

Functions.

Math 2 3 0 3 Contemporary

Mathematics

MATH 1.1 This course aims to integrate mathematics

theories with reality. The approach is toconceptualize the concepts of Matrices,

Linear Programming, Probability,Sampling and Distributions, Measures ofOrder, Hypothesis Testing, Similarity

Measurement and Shapes, Exponential and

Logarithmic functions, Ratios, Symmetry,Tilings, Sequences and Series, Conic

Sections and Distances.

Math 2.1 3 0 3 Plane and

Spherical

Trigonometry

Trigonometric Functions; Identities andEquations; Solutions of Triangles; Law of

Sines; Law of Cosines; InverseTrigonometric Functions; Spherical

Trigonometry.Math 3 5

units

0 5

units

PreCalculus

Algebra

NSAE Sets; Methods of Proof and Disproof; the

Real and Complex Number Systems;Polynomials and Rational Expressions;

Mathematical Induction and the Binomial

Theorem; Rational Exponents andRadicals; Equations in One Variable;

Systems of Equations; Inequalities;

Functions and Relations; Algebraic

Functions; Exponential and LogarithmicFunctions

Math 4 3 0 3 Advanced

AlgebraMath

1.7/Math 2

This course provides a rigorous study ofthe Fundamental Concepts of Functions

leading to advanced concepts of Special

Functions. The course includes Axioms ofOrder, Complex Numbers, Equations and

Inequalities, circles and Conic Sections,

Functions and their Graphs, PolynomialFunctions and Equations, and Exponential

and Logarithmic Functions

Math 5 4 0 4 College

Trigonometry

Math 3 Functions and relations; algebraic

functions; exponential and logarithmicfunctions; trigonometric functions of

angles; trigonometric functions of real

numbers.

Math 6 3 0 3 Plane and

SolidMath 2/ Math

4

This course covers the study of points,

lines and planes, including angles that


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Geometry serve as a springboard for understandingSolid Geometry and Analytic Geometry. It

also includes the construction of 2D and

3D shapes and their properties.

Math 6.1 3 0 3 Plane

GeometryConstructions; 2D Shapes; Similarity andCongruence: Triangles, test for Area:

Symmetry; Circles: Symmetry Properties,

Angle Properties

Math 6.2 3 0 3 Solid

Geometry

Math 6.1 Constructions; 3D Shapes; Prisms.

Cylinder; Pyramids; Cones and Spheres;

Similarity and congruence: Tests in

Volume: Symmetry

Math 6.4 3 0 3 Analytic

Geometry(Math 1.7 &

Math 2.1)

Math1.3/Math 1.4

Coordinate system; Distance formula;Lines; Slope; Equations of a Line;

Perpendicular and Parallel Lines, Circles;Conic Sections; Translation of Axes;Limits and Continuity. Optional:

Differentiation and Integration.Math 6.5 2 0 2 Solid

MensurationMath 1.7 and

Math 2.1

This course deals with the concept of lines

and planes; Cavalieris and Volume

theorems; formulas for areas of planefigures, volumes for solids; volumes and

surfaces areas for spheres, pyramids, and

cones; zone, sector and segment of a

sphere; theorems of Pappus.

Math 7 3 0 3 History of Mathematics

Math 4 History and philosophy of Mathematicsfrom ancient, medieval, present andmodern era; Mathematicians during ancient

and modern times.

Math 7.1 3 0 3 Mathematics

of

Investments

To be constructed

Math 7.2

Must have

bigger

number

3 0 3 Industrial

Mathematics

Math 9.2 Topics here include setting up partialdifferential equations and boundary

conditions, dimensional analysis, scaling,

perturbation expansions, boundary value

problems, Fourier series, symmetryreductions. For students of mathematics,

engineering, or any other related discipline,

this will be a great introduction tomodeling the real world.

Math 9.1 4 0 4 Differential

CalculusThis course introduces to students thefundamentals of calculus. It covers the

following topics: Rate of Change and

Slope; Limits; the Derivatives and theirapplications; Continuity and Graphs;


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Partial Derivatives; Lagrange Multipliers;Method of Least Squares; Second

Derivative; Curve Sketching Techniques;

Optimization; Maxima and Minima;Related rates and other Applications

Calculus 2

3

units

Math 9.1

4 0 4

3 units

Math

9.1

Antiderivatives and Indefinite Integral;

Integration by Substitution; Differential

Equations: Growth and Decay; DefiniteIntegral; Fundamental Theorem ofCalculus; Area between Curves;

Applications in Business and Economics;

Integration by Parts; Partial Derivatives;Lagrange Multipliers; Method of Least

Squares; Double Integrals of Rectangular

Regions.

Math 20 4 0 4 Calculus for

Biosciences

Math 5 This course is the first treatment of major

topics in Calculus, meant to be anintroduction to basic aspects of functions,

limits, differentiation and integration, anddifferential equations in view of somepotential applications to Biosciences.

Math 10 6 0 6 Calculus W/

Analytic

Geometry I

Math 5 This course is an introduction to Calculus

with Analytic Geometry. It covers Lines,

Circles, Conic Sections, Special Functions,

Limits, Continuity, Derivatives and theirApplications, Differentials,

Antiderivatives, Definite Integrals and their

Applications.

Math 11 6 0 6 Calculus withAnalytic

Geometry II

Math 10 This course covers the Dervatives andIntegrals of Transcendental Functions,Techniques of Integration, Approximations

of Definite Integrals, Polar Coordinate

System, Vectors, and Curves and Surfaces

in Three Dimensional Space

Math 12 6 0 6 Calculus with

Analytic

Geometry III

Math 11 Calculus of Functions of Several Variables,

Sequences, Infinite Series and PowerSeries.

B. MATHEMATICS MAJOR SUBJECTS

Course

No.

Credit Course Title Prerequisites Course Description

Le

c

Lab Total

Math

80

2 1 3 LaTex and

Mathematical

Software

This course deals with an introduction tocomputer concepts and fundamentals;

miktex and texniccenter softwares;

typesitting mathematical equations, graphs


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and interfacing of files and documents; andintroduction to softwares used in

mathematical computing.

Math

100

3 0 3 Logic and Set

Theory

Math 12/

Math 9.2

Mathematical Logic; Sets and theirProperties; Relations and Functions;

Cardinal Numbers; Ordering Relations.

Math

101

3 0 3 Problem

Solving

Math 10 This course aims to provide future

elementary teachers with holistic experienceof Mathematical Problem Solving and

Investigations. The topics include Problem

Solving Framework, Problem Solving

Process, routine and Non-routine Problemsand Problem Formulation.

Math

105

3 0 3 Discrete Math Math 10 Logic and Proofs; Sets and Numeration

Systems, Algorithms, Counting methods and

Recurrence Relations; Introduction to GraphTheory

Math

106

3 0 3 Number

Theory

Math 100 Properties of Natural Numbers; the System

of Integers as a Well-Ordered IntegralDomain; Divisibility; Congruences;

Diophantine Equations; Quadratic Residues;

Distribution of Primes; Algebraic NumberFields.

Math

111

3 0 3 Abstract

Algebra I

Math 100 Binary Operations; Groups; Subgroups;

Permutation Groups; Cyclic Groups;

Lagranges Theorem; Homomorphism;Isomorphism; Automorphism; Cayleys

Theorem; Direct Products; Cosets; Normal

Subgroups; Factor Groups; Correspondence

Theorem.

Math

112

3 0 3 Abstract

Algebra II

Math 111 Rings; Subrings; Integral Domains;Homomorphism of Rings; Ideals; Quotient

Rings; Field of Quotient of an Integral

Domain; Ideals; Prime Fields; Rings of

Polynomials; Factorization of PolynomialsOver a Field; Unique Factorization Domain;

Extension Fields; Splitting Fields.

Math

114

3 0 3 Linear

Algebra I

Math 100 Matrices and Systems of Linear Equations;Vector Spaces; Basis; Subspace; Linear

Transformations; Determinants; Adjoint;

Eigenvalues and Eigenvectors; NormalForm; Linear Functionals.

Math

115

3 0 3 Linear

Algebra II

Math 114 This is a continuation of Linear Algebra I.

Topics include linear functionals; BilinearForms; Inner Product Spaces; Orthogonal

and Unitary Transformations; Gram-Schmidt Orthogonalization Process;

Application to Linear Programming; Graph

Theory and Numerical Analysis.

Math

116

3 0 3 Modern

Geometry

Math 114 &

Math 111

Euclidean and Affine Geometry on thePlane, Euclidean Geometry on the Sphere,

Introduction to Finite Geometries and to the


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Non-Euclidean Hyperbolic and EllipticGeometries.

Math

118

3 0 3 Linear

Programming

Math 100 The Simplex Method; Duality; Geometry of

Linear Programs; Dual Simplex Method;

Parametric Programming; IntegerProgramming; Network Analysis including

PERT-CPM; Algorithms for Linear

Programming; Decomposition and Upper-Bound Technique.

Math

119

3 0 3 Non-Linear

Programming

Math 118 Properties of Convex Set and Functions;

Constrained and Unconstrained

Optimization; Kuhn-Tucker Conditions;

Quadratic Programming; ConvexProgramming; Saddle-Point Theorems;

Algorithms for Non-Linear Programming.

Math

121

3 0 3 Real Analysis

I

Math 100 The Real Number System; Lebesgue

Measure and Integration; Differentiation;Metric Spaces; Topological Vector Spaces;

Stone-Weierstrass Theorem.

Math

122

3 0 3 Real Analysis

II

Math 121 This is a continuation of Real Analysis I.

Topics include classical Banach Spaces,Topics in Measure Theory and Integration

Theory.

Math

123

3 0 3 Complex

Analysis I

Math 121 The Complex Number System; Complex

Integration and Differentiation; CauchysTheorem; Analytic Functions; Harmonic

Functions; Conformal Mappings; Infinite

Series; Singularity; Residue Theory.

Math

124

3 0 3 Complex

Analysis II

Math 123 This is a continuation of Complex Analysis

I. Topics include Poisson Integral Formulaand its Applications; Inverse Functions;

Analytic Continuation; Entire Functions;

Infinite Products; Hadamard FactorizationTheorem; Families of Analytic Functions;

the Prime Number Theorem

Math

125

2 1 3 Numerical

Analysis

Math 114 Solution of Linear Systems; Iterative

Methods of Solving Equations; LinearDifference Equations; Application to

Solution of Polynomial Equations;Difference and Integral Formulas; Minimal

Solutions to Ordinary Differential

Equations, Round-off Error Bounds

Math

126

3 0 3 Topology Math 221 Topological Spaces; Continuous Functions;

Product Spaces; Quotient Spaces;

Convergence Structures; Nets and Filters;

Separation Axioms; Countability Properties;

Connectedness, Metrizable Spaces.

Math

129

3 0 3 Combinatorial

Mathematics

Math 111 Fundamentals of Combinatorial

Mathematics; Permutations and

Combinations; Generating Functions;Principles of Inclusion and Exclusion;

Recurrence Relations; Matrices of Zeros and

Ones; Partition Function; Orthogonal Latin

Squares; Combinatorial Designs, othertopics.


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Math

131

3 0 3 Graph Theory

I

Math 100 Graphs and Associated Matrices;Subgraphs; trees; Connectivity;

Traversability; Oriented Graphs; Kernels;

Domination and Independence; Matching

Theory; Groups and Graphs; Coloring.

Math

132

3 0 3 Graph Theory

II

Math 131 This is a continuation of Graph Theory I.

Topics include Planar Graphs; Directed

Graphs; Tournaments; Networks; CycleSpaces; Bond Spaces; Applications of

Graph Theory; other topics

Math

133

3 0 3 Actuarial

Mathematics

Stat 110

(Probability

Theory I)

This course covers the mathematical theory

of life contingencies involving single-lifefunctions, mortality, life annuities and

insurances, and reserves,

Math

150

2 1 3 Mathematical

Modeling

Math 151 Mathematical modeling using Graphical,

Numerical, Symbolic, and Verbal

Techniques to describe the explore real

world data and phenomenon.

Math

151

2 1 3 Differential

Equations

Math 11 This course deals with the techniques in

finding for the solution of a Differential

Equation, Existence, Uniqueness anddependence Theorems; Homogeneous and

Non-Homogeneous Differential Equation,

Linear Differential Equation, Applications.

PREPARED BY: MATHEMATICS DEPARTMENT

NOTED BY:

JAYROLD P. ARCEDE Ph.D

CHAIR, MATH DEPT.

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