This course is designed to improve the students¿ mastery of the fundamental operations of arithmetic, including whole numbers, fractions, decimals, mixed numbers and percentages. Emphasis is placed on number manipulation and applications relating to process.

This course is a corequisite Math course in which the Intermediate Math course is coupled with the credit-bearing College Algebra course (IHL Policy 608E). Students will engage in extra time for mandatory labs and tutoring to help them master the content necessary to successfully complete MATH 103. Upon successfully completing this course, students will receive credit for the Intermediate Math and the College Algebra course. The course will consist of an accelerated refresher on linear equations and inequalities and their graphs, absolute value equations and inequalities, exponents, and polynomials, factoring, rational expressions, radicals, and quadratic equations; followed by an analysis of graphs and functions; polynomial functions; rational, power, and root functions; inverse, exponential, and logarithmic functions with integrated refresher content as necessary.

The function concepts, solving quadratic equations, graphing the quadratic function, inequalities, absolute value, absolute inequalities, Fundamentals theorem of Algebra, roots, factors, systems of equations and matrices, math induction and Binomial Theorem, arithmetic and geometric progressions, logarithms, complex numbers, partial fractions, and applications of all topics.

Right and oblique triangular solutions, identities, trigonometric equations, systems of angular measurements, and applications.

MATH 113 (3) Quantitative Reasoning. Quantitative Reasoning is a general education course designed for students in non-STEM degree pathways. The course empowers students' reasoning with data in relation to real-life situations, arts, health, science, and social issues. It enhances critical thinking and quantitative literacy while developing awareness about rules or principles guiding the understanding and evaluation of real-life problems. It is designed to teach students a wide range of general mathematics. Problem-solving and critical thinking skills, along with the use of technology, will be emphasized and reinforced throughout the course in solving applied problems. Topics include: algebra, concepts of set theory, modeling, geometry, measurement, probability, statistics, simple regression analysis, and making predictions with data.

Polynomial equations, exponents and radicals, logarithms, quadratic equations, inequalities, complex numbers, permutations and combinations, probability, determinants, simultaneous linear equations, induction, binomial theorem, progressions and series, triangular solutions, identities, trigonometric equations, systems of angular measurement applications.

Introductory ideas for students of education, compound statements, sets and subsets, partitions and counting, elementary probability theory.

Functions, limits, continuity, differentiation, applications, basic analytic geometry, algebraic, exponential and logarithmic functions, integration, applications, series and sequences, improper integral. Specific applications.

Study of various numeration systems, rational and real numbers, fraction and decimal algorithms, ratios, percentages, consumer mathematics, introduction to problem-solving and logic, use of patterns and Venn diagrams.

Functions, limits, continuity, differentiation, limiting forms, applications, properties of continuous functions, analytical geometry and integration. The laboratory component is designed to reinforce the lecture component with activities requiring the use of technology in the form of computers with selected software and graphing utilities.

Infinite Sequences and Series, Tests of Convergence or Divergency, Power Series, Vectors and the Geometry of Space, Vector Valued- Functions, Partial Derivatives: Chain rule, Directional Derivatives, Gradient, Tangent Planes and Differentials. The laboratory component is designed to reinforce the lecture component with activities requiring the use of technology in the form of computers with selected software and graphing utilities.

Continuation of Functions of several variables and partial differentiation; multiple integrals, vector calculus and integration in vector fields. The laboratory component is designed to reinforce the lecture component with activities requiring the use of technology in the form of computers with selective software and graphing utilities.

Introduction, frequency distributions, location measures, variation, symmetry, skewness, peakedness, index numbers, probability, theoretical distributions, sampling, estimation, tests of hypotheses, non-parametric tests, linear regression, coefficient of correlation, time series analysts.

Sets and relations, natural number sequence, extension of natural number to reals, logic, informal axiomatics, Boolean algebra, interval and set theory, algebraic theories, first order theories.

Basic notions of lines, angles, triangles, circles and proofs. Stress is placed on synthetic methodology and reasoning.

Introduction to concepts of probability and statistics required to solve problems in various disciplines; mathematical basis for probability and statistics includes axioms of probability, continuous sampling distributions, and discrete probability, hypothesis testing, confidence intervals, probability estimations for risk assessment, data processing and statistical inference, statistical techniques of data analysis, simple and multiple regression model development; stochastic processes, emphasis is on the application of probability, statistics and reliability to rational decision making, data analysis and model estimation in engineering context.

Basic concepts of modern algebra, preliminaries, elementary ideas of groups, rings, integral domains and fields.

Euclidean, non-Euclidean, projective and affine geometrics with emphasis on the appropriate postulates and the postulational method. Transformation theory.

A theoretical study of equations, matrices, vector spaces, inner product spaces linear transformations bilinear and quadratic forms, and eigenvalues.

Sets and functions, continuity, integration, convergence, differentiation, and applications to geometry and analysis, differential geometry, and vector calculus.

Random variables, conditional probability and stochastic independence, special distributions.

Estimations, order statistics, limiting distributions, statistical hypotheses, variance, normal distribution theory, point and interval estimation, sampling, regression and correlation.

Introduction to differential equations, first-order differential equations, higher-order differential equations, series solutions of linear equations, the Laplace transform and systems of linear first-order differential equations.

This course includes topics pertinent to success in problem solving for Secondary Mathematics Education majors: arithmetic and basic algebra, geometry, trigonometry, analytic geometry, functions and their graphs, calculus, probability and statistics, discrete mathematics, linear algebra, computer science, and mathematical reasoning and modeling. In addition to review of content that pertains to the aforementioned topics, students will investigate test taking skills and methods of problem solving. Underlying focus will be to develop students' mathematical communication skills through regular class participation and peer evaluation activities.

Materials and sources of value to prospective teachers of high school, middle school and junior high school mathematics, reports, current articles, state-adopted textbooks, yearbooks and histories, special problems in teaching geometry and algebra.

The provisions to the student of an opportunity to discuss pertinent trends and ideas in mathematics, and to evaluate the experience he has had through study and practice during his previous years of training in mathematics.

Topics in elementary number theory, finite fields, and quadratic residues. Cryptography public key, primality and factoring, elliptic curves.

Groups rings, integral domains, modules, vector spaces, fields, linear transformations, special topics in group, ring, and field theory.

Heat equations, Laplace¿s equation, Fourier series, wave equation, Strum-Liouville eigenvalue problems, nonhomogeneous problems, method of Green¿s functions, infinite domain problems and the methods of characteristics for wave equations.

Real number system, basics, numerical sequences and series, continuity, differentiation, Reimann-Stieltjes integral, sequences and series of functions, special series, functions of several variables, the Lebesgue theory.

Theory of arithmetical meanings, learning and rational, applied meanings, current trends.

Complex numbers and representations, point sets, sequences, functions, analytic functions of one complex variable, elementary functions, integration, power series, calculus of residues, conformal representation, applications.

Elementary set theory, ordinals and cardinals, topological spaces, cartesian products, connectedness, special topologies, separation and covering axioms, metric spaces, convergence, compactness, function spaces, compete spaces, elementary homotopy and homology theory.

Learning programming, network analysis, PERT-CPM, dynamic programming, queuing theory and decision analysis.

Historical development of numbers and numerals, computation, geometry, algebra, trigonometry, calculus, modern mathematics.