- Intermediate Algebra
- Elementary Statistics
- Applied Probability
- Finite Mathematics with Applications
- Trigonometry for Calculus
- Introduction to Mathematical Computation
- Pre-Calculus and Introduction to Analytic Geometry
- First Year Calculus (Calculus I)
- Business Calculus
- Mathematical Writing
- Mathematics and Computer Science Problem Seminar
- Dynamical Systems and Chaos
- Computer Musings Lecture Series

Algebra Review

- Video Lectures: Math 160 (University of Idaho)

Intermediate Algebra

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

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

Elementary Statistics

- Video lectures (De-Anza College)
- Course website

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.

Course covers: Sampling and data. Statistical graphs, quartiles and percentiles, mean, median, mode, variance and standard deviation. Basic probability, independent and dependent events, addition and multiplication rules. Discrete random variables, discrete probability distribution functions, expected value, binomial probability distribution function. Continuous random variables, continuous probability distribution functions, uniform probability distribution, exponential probability distribution. The normal probability distribution function, standard normal probability density function. Central limit theorem for averages and sums. Confidence intervals. Hypothesis testing. The Chi-Square distribution function. Linear regression and correlation.

Applied Probability (5 lectures)

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

Finite Mathematics with Applications

- Video Lectures: Math 1313 (University of Houston)

Trigonometry for Calculus

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

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

Introduction to Mathematical Computation

- Video Lectures: Math 309 (San Francisco State University)
- Course website

Throughout the course we will illustrate application of software in typical undergraduate mathematical subjects such as calculus, probability, linear algebra, and number theory. Further, we will move to structural programming. We conclude the course by illustrating elements of contemporary platform independent language, java.

**No programming experience required**

Course covers: Basic commands in Mathematica, Mathematica in Calculus, Mathematica in Probability, Mathematica and Linear Algebra, Mathematica and Number Theory, Mathematica and structural programming, Introduction to Java.

Note: Links to lectures 6 - 17 are missing. You can access them by changing the last number of the link to the first 5 lectures. Example: to access lecture 12 use address http://130.212.40.150:8080/ramgen/mathematica/lecture12.rm, etc.

Pre-Calculus and Introduction to Analytic Geometry

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

Course covers: equations and identities, graphs, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, analytic geometry.

First Year Calculus (Calculus I)

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

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

Business Calculus

- Video Lectures: Math 1314 (University of Houston)

Course covers limits, one-sided limits and continuity, the derivative, basic rules of differentiation, the product and quotient rules, the chain rule, higher order derivatives, basic applications of derivative, marginal functions in economics, applications of the first derivative, applications of the second derivative, curve sketching, absolute extrema, optimization, applications with exponential functions, antiderivatives, integration by substitution, area under the curve - Riemann Sums, the fundamental theorem of calculus, evaluation of definite integral, area between two curves, functions of several variables, partial derivatives, relative extrema.

Mathematical Writing (by Donald E. Knuth!)

- Video lectures: CS209 (Stanford University, 1987)
- Lecture notes (pdf)

"I also gave a class called

*Mathematical Writing*, just for one quarter," says Knuth. "The lectures are still of special interest because they feature quite a few important guest lecturers." This collection contains thirty-one tapes.

Mathematics and Computer Science Problem Seminar (by Donald E. Knuth!)

- Video lectures: CS204 (Stanford University, 1985)
- Notes on problems (pdf)

According to D. E. Knuth course is given only once in two years because it takes him two years to think of good enough problems. The goal of the course it to understand problem solving in general and not just to solve those 5 problems and to get into as many of the different areas of computer science research as possible.

"This was an experimental project where we'd have three or four cameras in a basement studio and we would film classes of about an hour," says Knuth. "We got a bunch of our brightest students and gave them extremely difficult problems. You could literally

*see*the Aha taking place. People can watch the problem-solving process as it occurred." Over 25 hours of these sessions are available for viewing.

Dynamical Systems and Chaos

- Video Lectures: Math 614 (University of Texas A&M)
- Course website

Then we will study bifurcations on the example of dynamics of quadratic maps. The quadratic family will be used to demonstrate the transition to chaos and the main features of chaotic behaviour. We will touch Sarkovsii's Theorem and Newton's Method.

Elements of Symbolic Dynamics and subshifts of finite type will be considered. Then we will move to fractals and discuss fractal dimension and related topics. After that we will introduce Holomorphic Dynamics and the main objects such as Julia sets and the Mandelbrot set. Time permitting, we will consider some rational maps in dimension two and higher. Henon map will be considered, as well as some maps arising in the theory of fractal groups, and the Smale horse shoe map. We will consider also spectra and spectral measures related to such groups and to fractal sets like Sierpinski gasket or Cantor set.

Computer Musings Lecture Series (by Donald E. Knuth)

?These lectures I'?ve given have been inspired and shaped by the questions and responses of the audiences to whom I spoke, and I want to keep them alive,prof. D.E.Knuth explains. We'?ve got these tapes and the world is going digital; Stanford Centre for Professional Development has the talent and expertise to convert them. I feel that archiving is important. I'?ve learned from archived lectures and classes myself, so I think others can learn from these.

A sampling of musings includes:

- Dancing Links
- Fast Input/Output with Many Disks, Using a Magic Trick
- MMIX: A RISC Computer for the New Millennium
- The Joy of Asymptotics
- Bubblesort at random (one-dimensional particle physics)
- Trees, Forests, and Polyominoes
- Finding all spanning trees

"Other" Donald E. Knuth Lectures

Also available are two five-session short courses about TeX (1981); twelve lectures about the implementation of TeX (1982); video recordings of eight history sessions about Computer Science at Stanford, taped in 1987 and featuring many alumni of our department; and some reminiscences by Professors Feigenbaum, Floyd, Golub, Herriot, Knuth, McCarthy, Miller, and Wiederhold about the founding of Stanford's Computer Science Department,

*The Living Legends*(1997).

Questions from audience and students are important to the learning process, according to Knuth. Sometimes the expression of a more mature idea isn't the most interesting or effective way to learn you may learn more from how a professor reacts to an idea or a question. He pauses, and then adds, People might learn a lot from watching me fumble around to answer a question.

## 1 comments:

Thanks for linking up. Trigonometry is used to define trigonometric functions. Trigonometric functions describe the relationships between the angles and sides and are also applied to cyclical phenomena, such as waves.

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