무료 온라인 수학 강좌 사이트

무료 온락인 수학강의 사이트들을 정리해 보았습니다.
고등학교 과정부터 대학에서 들을 수 있는 강의까지 있습니다.
강좌에 관한 간단한 소개글들이 있으므로 읽어보시고, 제가 간단하게 어떤 내용들이 있는지 적었습니다.)

Algebra Review (수학 10 수준의 내용입니다.)

• Video Lectures: Math 160 (University of Idaho)

Coursecovers: factoring, interval notation, definition of function,functions, piece-wise defined functions, function composition,quadratic functions, solving quadratic functions. Slope of the line,equation of the line, parallel and perpendicular lines. Law ofexponents, properties of logarithms. Applications to exponentialfunction, exponential growth and decay. Solving systems of equations bysubstitution and elimination.


Intermediate Algebra (역시 수학 10 수준의 내용입니다.)

• Video Lectures: Math 108 (University of Idaho)
• Course website

Theprimary purpose of Intermediate Algebra is to improve your skills andcompetency in algebra so that you will be successful in calculus, theother math courses required for your major, and in the courses that usemathematics. Another goal is to help you develop your mathematicallearning skills so that you will be more confident in futuremathematical courses.

Course covers: the real numbers, linearequations, linear inequalities and absolute value, linear equations andinequalities in two variables, systems of linear equations, exponents,polynomials and polynomial functions, factoring, rational expressions,roots and radicals, quadratic equations and inequalities.



Applied Probability (요건 확률에 대해 관심이 많은 고등학생이나 확률과목을 듣는 대학생에게 유용할 듯 합니다.)

• Video Lectures at ArsDigita University
• Mirror at ArsDigita
• High Speed Mirror at Internet Archive
• Course website
  

Focuseson modeling, quantification, and analysis of uncertainty by teachingrandom variables, simple random processes and their probabilitydistributions, Markov processes, limit theorems, elements ofstatistical inference, and decision making under uncertainty. Thiscourse extends the discrete probability learned in the discrete mathclass. It focuses on actual applications, and places little emphasis onproofs. A problem set based on identifying tumors using MRI (MagneticResonance Imaging) is done using Matlab.


Finite Mathematics with Applications
(실제 수학이 적용되는 여러 가지 예들을 소개하고 있습니다. 똑똑한 고등학생들이나 대학생에게 유용할것 같습니다.)

• Video Lectures: Math 1313 (University of Houston)
  

Coursecovers slopes, equations and graphing of lines, linear depreciation,cost, revenue and profit functions, intersection of lines, break-evenanalysis, the method of least squares, graphing linear inequalities,graphing systems of linear inequalities, linear programming problems,graphical solution of linear problems, simple interest, future value,present value, and effect rate, annuities, amortization and sinkingfunds. Set notation and terminology, set operations, Venn diagrams,number of elements in a set, the multiplication rule, permutations andcombinations. Experiments, events and sample spaces, definition ofprobability, rules of probability, use of counting technique,conditional probability, independent events, Bayes' theorem,distributions of random variables, expected value, odds, variance andstandard deviation, Chebyshev's inequality, the binomial distribution,the normal distribution, applications of the normal distribution.


Trigonometry for Calculus (미적분학을 위한 기초 삼각함수에 관한 강좌입니다.)

• Video Lectures: Math 144 (University of Idaho)
• Course website
  

Thegoal of this course is to prepare you for the trigonometry that youwill encounter in calculus. During this one credit course intrigonometry, you will learn how to evaluate trigonometric functions,sketch the graphs of the sine, cosine and tangent functions, study theinverse trigonometric functions and much more.

Course covers theCartesian coordinate system, functions, angle and radian measure,special right triangles, the unit circle, the trigonometric ratios,graphs of trig. ratios, periodic functions, fundamental trigonometricidentities and inverse trigonometric functions.



Pre-Calculus and Introduction to Analytic Geometry
(미적분학을 준비하는 학생들에게 기초가 될만한 내용입니다. 수1 정도의 수준입니다.)

• Video Lectures: Math 143 (University of Idaho)
• Course website

Theprimary purpose of Pre-Calculus and Analytic Geometry is to improveyour skills and competency in algebra so that you will be successful incalculus, the other math courses required for your major, and in thecourses that use mathematics. Another goal is to help you develop yourmathematical learning skills so that you will be more confident infuture mathematical courses.

Course covers: equations andidentities, graphs, functions and their graphs, polynomial and rationalfunctions, exponential and logarithmic functions, analytic geometry.


First Year Calculus (Calculus I) (미적분학 강의라고 보시면 됩니다. 수2와 심화 미적분 내용 + 알파 입니다.)

• Video Lectures: Math 226.01 (San Francisco State University)
• Course website

Thecentral object of the study in calculus is the concept of a function.Functions are used to describe the real world around us. Calculusintroduces two fundamental concepts which enable us to describe andinvestigate functions. These are: the derivative and the integral. Thederivative describes the behavior of a function at a particular time.The integral carries information about the history of a function.

Coursecovers: limits, limit laws, continuity, limits involving infinity,rates of change, derivatives, differentiation rules, product andquotient rules, rates of change in science, derivatives oftrigonometric functions, the chain rule, implicit differentiation,logarithmic differentiation, maxima and minima, mean value theorem,L'Hospital's rule, optimization problems, areas and distances, definiteintegral, fundamental theorem of calculus.