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This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn't get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you've hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Combinatorial analysis Textbooks
- Resource Type:
- e-book
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e-book
Think DSP is an introduction to Digital Signal Processing in Python. The premise of this book (and the other books in the Think X series) is that if you know how to program, you can use that skill to learn other things. The author is writing this book because he thinks the conventional approach to digital signal processing is backward: most books (and the classes that use them) present the material bottom-up, starting with mathematical abstractions like phasors.
- Subjects:
- Electrical Engineering and Computing
- Keywords:
- Signal processing -- Digital techniques -- Data processing Python (Computer program language) Textbooks
- Resource Type:
- e-book