This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.
Mathematics Textbooks and Full Courses
Mathematics Textbooks and Full Courses Collection Resources (256)
Online Statistics: An Interactive Multimedia Course of Study is an introductory-level statistics book. The material is presented both as a standard textbook and as a multimedia presentation. The book features interactive demonstrations and simulations, case studies, and an analysis lab.
Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.
Human Education is about holistic approach in the preparation of human beings to educate the unborn child through adequate care, nutrition and safety, before birth and once born, to enable a growing being to survive the challenges of life as they present themselves. Subjects are geared for critical thinking and for immediate application of acquired knowledge for their own survival, and not only for acquiring a certificate. This is urgent.
Elementary Statistics is an introduction to data analysis course that makes use of graphical and numerical techniques to study patterns and departures from patterns. The student studies randomness with emphasis on understanding variation, collects information in the face of uncertainty, checks distributional assumptions, tests hypotheses, uses probability as a tool for anticipating what the distribution of data may look like under a set of assumptions, and uses appropriate statistical models to draw conclusions from data. The course introduces the student to applications in engineering, business, economics, medicine, education, the sciences, and other related fields. The use of technology (computers or graphing calculators) will be required in certain applications.
This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)
This course is a self-contained introduction to statistics with economic applications. Elements of probability theory, sampling theory, statistical estimation, regression analysis, and hypothesis testing. It uses elementary econometrics and other applications of statistical tools to economic data. It also provides a solid foundation in probability and statistics for economists and other social scientists.
Introductory survey of quantitative methods (QM), or the application of statistics in the workplace. Examines techniques for gathering, analyzing, and interpreting data in any number of fieldsĺÎĺ from anthropology to hedge fund management.
Full course of Algebra 1 is presented online by Georgia Virtual Learning. Audio, video, text, games and activities are included to engage ninth grade students in learning.
My goal is to merge New York State standards with Common Core Standards and Integrated Algebra Regent Standards for our 8th grade curriculum.
This course covers descriptive statistics, the foundation of statistics, probability and random distributions, and the relationships between various characteristics of data. Upon successful completion of the course, the student will be able to: Define the meaning of descriptive statistics and statistical inference; Distinguish between a population and a sample; Explain the purpose of measures of location, variability, and skewness; Calculate probabilities; Explain the difference between how probabilities are computed for discrete and continuous random variables; Recognize and understand discrete probability distribution functions, in general; Identify confidence intervals for means and proportions; Explain how the central limit theorem applies in inference; Calculate and interpret confidence intervals for one population average and one population proportion; Differentiate between Type I and Type II errors; Conduct and interpret hypothesis tests; Compute regression equations for data; Use regression equations to make predictions; Conduct and interpret ANOVA (Analysis of Variance). (Mathematics 121; See also: Biology 104, Computer Science 106, Economics 104, Psychology 201)
Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The Geometry curriculum is available below.
This course has been designed to help students focus learning on specific areas of improvement. Unlike a typical college course where you would complete lessons in chronological order, this course allows you to focus on specific skills. Modules include: Arithmetic Review, Percents, Geometric Figures, Measurement, and Statistics
Students will take active roles in learning the game of chess and improving their skills, ability, and knowledge of the game. Students will read the course material, complete practice drills for each module, complete and submit all assessments and submit properly recorded (notated) games that they played. Course content includes: rules, strategy, tactics and algebraic notation (the 'language' of chess).
This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
This resource is a collection of short closed-captioned lectures that accompany the power points covering most of chapters 1,2,3, 6, 9, 11, 12, and 13 of the OpenStax Introductory Statistics book. The Power Points are provided in both .PPT and .PDF format to accommodate downloading ease. The notes are in .DOC format.
This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.
This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)