|
|
|
|
|
|
|
|
|
|
Course Criteria
Add courses to your favorites to save, share, and find your best transfer school.
-
3.00 Credits
Logic, sets, mathematical induction, relations, functions, Boolean algebra and rudiments of combinatorics and graph theory are covered. Course Objectives (1) Apply logic to complete and use truth tables for expressions involving logical connectives. (2) Construct direct and indirect (contradiction and contraposition) proofs, and induction proofs. (3) State and interpret the definitions of binary relation, reflexive, symmetric, transitive, equivalence relation, equivalence class, class representative, and partition. (4) Use set notation, including the notations for subsets, unions, intersections, differences, complements, cross (Cartesian) products, power sets, and Venn diagrams. (5) State and classify the definitions of one-to-one and onto. (6) State and interpret the Quotient-Remainder Theorem and the mod function. (7) State and apply the Fundamental Theorem of Arithmetic and the Euclidean Algorithm. (8) Solve counting problems involving the multiplication rule, addition rule, permutations, and combinations with and without repetition. (9) Use counting methods to solve discrete probability problems. (10) Define and identify paths and circuits. (11) Define and construct isomorphism graphs and planar graphs. (12) Define and identify spanning trees and minimal spanning trees. (13) Define the laws of Boolean algebra.
-
3.00 Credits
System of equations, Gaussian procedure, matrix algebra, determinants, geometry of two and three dimensional vectors, vector space Rn, subspaces, linear independence and spanning, basis and dimension, eigenvalues and eigenvectors. Course Objectives (1) Add matrices, multiply matrices by a scalar, and multiply matrices together. (2) Solve a system of linear equations by means of elementary row operations on its augmented matrix. (3) Compute and use the rank of a matrix to decide if the equations are consistent, independent, or dependent. (4) Find the inverse of a matrix by means of row operations or decide if the inverse does not exist. (5) Define, describe, and use the determinant of matrix and evaluate it by means of elementary row operations. (6) Define and calculate the trace of a square matrix and use its properties. (7) Define and identify subspaces of R" and find dimension. (8) Determine if a given set of vectors is linearly dependent. (9) Determine the rank of a set of vectors and use the rank to decide if a set of vectors is independent, dependent, or spans a specified subspace. (10) Reduce a spanning set of a subspace to a basis and to extend a linearly independent set to a basis. (11) Define linear function, determine if a function is linear, and to determine the matrix of a linear function in the standard bases of the domain and range spaces. (12) Find bases for the nullspace, kernel, and range of a linear function. (13) Find the eigenvalues and eigenvectors of a matrix and to diagonalize it if possible. (14) Formulate application problems in the language of linear algebra and solve them.
-
3.00 Credits
No course description available.
-
1.00 - 3.00 Credits
Selected Topics in MATH
-
1.00 Credits
No course description available.
-
4.00 Credits
Sequences and series, polar coordinates, two and three dimensional vectors and curves, functions of several variables, partial differentiation, multiple integrals and applications. Course Objectives (1) Use the definition of an infinite series as the sum of an infinite sequence to construct the series. (2) Determine convergence or divergence of an infinite series by evaluating the limit of the nth partial sum for geometric and telescoping series. (3) Recognize geometric series, harmonic series, and alternating series. (4) Construct Taylor Series expansions and Taylor polynomial approximations. (5) Construct and use the first several terms of a series to approximate an integral. (6) Change from polar to rectangular coordinates and vice versa. (7) Represent and evaluate functions of two and three variables graphically, numerically, and by formulas. (8) Find the magnitude, direction and component form of displacement vectors. (9) Perform vector addition, subtraction, scalar multiplication, dot product, geometric and component forms cross product. (10) Use vector models for applications of velocity, force, work, finding angles between vectors, and projections. (11) Find partial derivatives using numeric, graphic, and algebraic computations. (12) Interpret units and signs of partial derivatives. (13) Use a Riemann Sum to approximate a double integral. (14) Interpret the two-variable integral as a volume under the graph of a function of two variables. (15) Set up and evaluate double and triple integrals over 2- and 3- dimensional regions. (16) Apply techniques real-world problems.
-
3.00 Credits
First order differential equations, linear differential equations, series solutions and transformation methods. Course Objectives (1) Define the relevant terms related to differential equations. (2) Evaluate first order differential equations using separation of variables, homogeneous equations, exact equations, and linear equations. (3) Apply first order differential equations as linear and nonlinear models. (4) Evaluate higher order linear differential equations with constant coefficient s including initial value and boundary value problems, Homogeneous equations and Nonhomogeneous equations with undetermined coefficients and variation of parameters. (5) Apply higher-order differential equations as linear and nonlinear models. (6) Define and employ Laplace transform, inverse transforms, the transform of derivatives, and various translations. (7) Evaluate higher order linear differential equations with variable coefficients including power series solution around an ordinary point and solutions about a singular point.
-
3.00 Credits
Vector spaces, Linear transformations and matrices, bilinear forms, inner product spaces, diagonalization and function of matrices. Course Objectives (1) Find the matrix of a linear transformation with respect to different basis (2) Compute eigenvalues and eigenvectors and use them to diagonalize matrices whenever possible (3) Utilize the concepts and applications of inner product spaces (4) Apply the diagonalization process to quadratic forms (5) Use calculators and computer programs to solve linear algebra problems (6) Construct rigorous mathematical proofs (7) Formulate application problems in the language of linear algebra and solve them
-
3.00 Credits
A calculus based course covering permutations and combinations; random variables; basic, discrete and continuous distributions; expected values and moments; sum of independent identical random variables; and selected topics on statistical estimation and inference. Course Objectives (1) Make use of basic statistical concepts and applications (2) Use probability theory, including permutations and combinations, to calculate probabilities (3) Examine various discrete probability distributions (4) Develop the Central Limit Theorem and be able to employ it (5) Find density functions to describe distributions of continuous random variables (6) Employ techniques of statistical inference and estimation
-
3.00 Credits
Introduction to semi groups, groups, rings, fields and algebras with emphasis on applications to the theory of computation. Course Objectives (1) Describe and apply the basic concepts of number theory including the division algorithm, Euclid's algorithm, primes, the unique factorization theorem, Euler's theorem, and Fermat's Theorem. (2) Understand and use modular arithmetic and the Chinese remainder theorem. (3) Define rings and fields and investigate the field of complex numbers. (4) State the definition of a group and give examples. (5) State, prove and use elementary theorems of groups. (6) Define and find subgroups. (7) State, prove, and use basic theorems of subgroups. (8) State and prove theorems regarding isomorphism, homomorphism, cyclic groups, and permutation groups. (9) Find cosets and prove theorems regarding cosets. (10) State and apply properties of normal subgroups and quotient groups. (11) State, prove, and use elementary properties of rings, ideals, and quotient rings.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Privacy Statement
|
Terms of Use
|
Institutional Membership Information
|
About AcademyOne
Copyright 2006 - 2024 AcademyOne, Inc.
|
|
|