# Online courses directory (648)

This course provides prospective college students with a primer in college level reading, writing, and mathematics. Whether a student is preparing to take a standardized placement test, or simply wishing to determine and improve his or her readiness to handle college-level work, this course can help to build mastery and confidence. Students may choose to work at their own pace across all three subject areas, or to select individual content areas. Pretests will determine any learning deficits, which can then be mastered through self-paced learning modules. Not forgetting the importance of the human touch, this course is overseen by a trio of reading, writing, and mathematics professors who will be available to assist and encourage students along their journey to college readiness.

This game-based course provides prospective students with a primer in college level reading, writing, and mathematics. Whether preparing to take a standardized placement test or simply improving readiness to handle college-level work, this course can help student build mastery and confidence.

This game-based course provides prospective students with a primer in college level reading, writing, and mathematics. Whether preparing to take a standardized placement test or simply improving readiness to handle college-level work, this course can help student build mastery and confidence.

This game-based course provides prospective students with a primer in college level reading, writing, and mathematics. Whether preparing to take a standardized placement test or simply improving readiness to handle college-level work, this course can help student build mastery and confidence.

Our lives are full of combinations. Combinatorial mathematics is just the science to deal with combinations of discrete items. As an ancient field, the history of combinatorial mathematics can be traced back over 4000 years to the age of the Great Yu in ancient China. Today, combinatorial mathematics is regarded as the basis of computer science since the algorithms in programming heavily rely on the analysis of the discrete elements.

Instead of relying on the traditional mathematical "theorem - proof" format, this course demonstrates various principles in an intuitive manner with ancient stories, the scenes of movies and even a magic show. What you’ll learn:

- The counting principles based on the basic operations “+”, “-”, “*”, “/”;
- Generating functions
- Recurrent number serials such as Fibonacci number, Catalan number, and more
- Pigeon hole principles
- Inclusion and exclusion principles
- Polya counting based on group theory

This course is based on a highly regarded on-campus Tsinghua class called Combinatorics, and is ideal for students who are interested in mathematics or computer science. Enroll today and learn the mathematical theory needed to solve the real-world problems!

我们生活的方方面面都充满着组合，而组合数学正是研究离散事物的学科。作为一个具有悠久历史的学科，组合数学的发展可以追溯到4000年前的大禹时代。而如今组合数学随着计算机学科的发展开启了新的篇章，由于程序算法的分析和实现正是基于对离散对象的分析，因此组合数学已经发展成为计算机学科的基础理论。

而本课程一改以往数学教学的“定理-证明”模式，引领大家由浅入深地逐步探索知识的源泉，这里有古代故事，有电影片段，甚至用魔术来演绎数学概念。而这些形式就是为了引领大家去感受数学的美。具体的教学内容包括：

- 基于四则运算的计数法则；
- 母函数；
- 递推序列，如斐波那契数，卡特兰数等；
- 鸽巢原理；
- 容斥原理；
- 基于群论的波利亚定理。

本课程的内容和大纲主要基于清华大学精品课《组合数学》，通过本课程的学习，学习者可以深入了解计数的抽象理论和具体方法，从而深入理解组合数学对计算机理论发展的推动作用。。

**FAQ**

**I don’t speak Chinese, can I learn the course?**

All the materials are in English. Though the original video was recorded in Chinese, the course team record the corresponding dubbing in English. All the audio and subtitles are processed to fit the English dubbing as much as possible, so that you can enjoy this wonderful course in English.

**What are the textbook and the reference books for this course?**

There is no textbook requirement for this course. The handouts distributed every week are critical. The following books are references

- Richard A. Brualdi; Introductory Combinatorics (5
^{th}edition), Pearson, 2009 - J.H.van Lint and R.M. Wilson; A course in Combinatorics, Cambridge University Press, 2001
- 卢开澄,《组合数学》第四版,清华大学出版社

**What is the grading breakdown?**

- 70% quizzes and exercises
- 30% final exam

**How can I get the certificate?**

If your final score is no less than 60.

**Do I need to know how to program to learn this class?**

Not necessary. This course is a math course which is based on fundamental theory. But to help the students to have the intuitive feel of the effects of the theory, we also provide a code lib that you can compare different implementations by running different programs.

This course is designed to prepare Saylor’s consulting educators to build K-12 subject courses that are aligned with the Common Core State Standards in English Language Arts & Literacy in History/Social Studies, Science and Technical Subjects and Mathematics. You will begin this course by gaining an overview of what the set of Common Core State Standards is, why Saylor is focused on developing courses around the Common Core State Standards, and the main benchmarks for ensuring that a course is compliant with the Common Core State Standards. In unit 2 of this course, you will look at the Common Core State Standards in detail and identify key takeaways from them. In unit 3 of this course, you will explore how to develop content that meets the Common Core State Standards and how to integrate the standards through the development of learning assignments based on specific texts and activities. In unit 4 of this course, you will take a look at the different assessment strategies often used for Common Core…

This course offers participants an opportunity to engage in a community of learners using an inquiry cycle focusing on math formative assessments as a strategy for implementing CCSS in math. It focuses on the implementation of a Classroom Challenge: a 1 – 2 day lesson developed by the Mathematics Assessment Project (MAP) based on formative assessment and the CCSSM.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

Example problems from random math competitions. 2003 AIME II Problem 1. 2003 AIME II Problem 3. 2003 AIME II Problem 4 (part 1). Sum of factors of 27000. Sum of factors 2. 2003 AIME II Problem 5. 2003 AIME II Problem 5 Minor Correction. Area Circumradius Formula Proof. 2003 AIME II Problem 8. Sum of Polynomial Roots (Proof). Sum of Squares of Polynomial Roots. 2003 AIME II Problem 9. 2003 AIME II Problem 12. 2003 AIME II Problem 13. 2003 AIME II Problem 10. 2003 AIME II Problem 11. 2003 AIME II Problem 14. 2003 AIME II Problem 15 (part 1). 2003 AIME II Problem 15 (part 2). 2003 AIME II Problem 15 (part 3). 2003 AIME II Problem 1. 2003 AIME II Problem 3. 2003 AIME II Problem 4 (part 1). Sum of factors of 27000. Sum of factors 2. 2003 AIME II Problem 5. 2003 AIME II Problem 5 Minor Correction. Area Circumradius Formula Proof. 2003 AIME II Problem 8. Sum of Polynomial Roots (Proof). Sum of Squares of Polynomial Roots. 2003 AIME II Problem 9. 2003 AIME II Problem 12. 2003 AIME II Problem 13. 2003 AIME II Problem 10. 2003 AIME II Problem 11. 2003 AIME II Problem 14. 2003 AIME II Problem 15 (part 1). 2003 AIME II Problem 15 (part 2). 2003 AIME II Problem 15 (part 3).

In this advanced math course, you will learn how to build solutions to important differential equations in physics and their asymptotic expansions. Armed with the tools mastered in this course, you will have a solid command of the methods of tackling differential equations and integrals encountered in theoretical and applied physics and material science.

The course is for engineering and physics majors. The course instructors are active researchers in theoretical solid-state physics.

This class explores sound and what can be done with it. Sources are recorded from students' surroundings - sampled and electronically generated (both analog and digital). Assignments include composing with the sampled sounds, feedback, and noise, using digital signal processing (DSP), convolution, algorithms, and simple mixing. The class focuses on sonic and compositional aspects rather than technology, math, or acoustics, though these are examined in varying detail. Students complete weekly composition and listening assignments; material for the latter is drawn from sound art, experimental electronica, conventional and non-conventional classical electronic works, popular music, and previous students' compositions.

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.

An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers.

This course presents material in discrete mathematics and computation theory with a strong emphasis on practical algorithms and experiential learning. Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. The CDM course is currently under development and we are making the course available while it is under development. Only one of the planned fifteen modules is currently available. The module on Groups that is currently available would appear mid-way through the complete course.