By John V. Guttag
This booklet introduces scholars with very little previous programming adventure to the paintings of computational challenge fixing utilizing Python and diverse Python libraries, together with PyLab. It presents scholars with abilities that may permit them to make efficient use of computational suggestions, together with many of the instruments and strategies of «data technological know-how» for utilizing computation to version and interpret info. The publication relies on an MIT direction (which turned the most well-liked direction provided via MITs OpenCourseWare) and was once built to be used not just in a traditional lecture room yet in a huge open on-line path (or MOOC) provided by way of the pioneering MIT-Harvard collaboration edX.
Students are brought to Python and the fundamentals of programming within the context of such computational options and strategies as exhaustive enumeration, bisection seek, and effective approximation algorithms. The publication doesn't require wisdom of arithmetic past highschool algebra, yet does imagine that readers are ok with rigorous considering and never intimidated by way of mathematical suggestions. even though it covers such conventional issues as computational complexity and easy algorithms, the e-book specializes in quite a lot of themes no longer present in so much introductory texts, together with details visualization, simulations to version randomness, computational innovations to appreciate information, and statistical strategies that tell (and deceive) in addition to similar yet really complicated subject matters: optimization difficulties and dynamic programming. advent to Computation and Programming utilizing Python can function a stepping-stone to extra complicated desktop technology classes, or as a simple grounding in computational challenge fixing for college kids in different disciplines.
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Additional resources for Introduction to Computation and Programming Using Python, Revided & Expanded
1. 1 Using bisection search to approximate square root This is a reasonable piece of code, but it lacks general utility. It works only for values denoted by the variables x and epsilon. This means that if we want to reuse it, we need to copy the code, possibly edit the variable names, and paste it where we want it. Because of this we cannot easily use this computation inside of some other, more complex, computation. Furthermore, if we want to compute cube roots rather than square roots, we have to edit the code.
How many different numbers can be represented by a sequence of length n? A sequence of length one can represent any one of ten numbers (0 - 9). A sequence of length two can represent one hundred different numbers (0-99). More generally, with a sequence of length n, one can represent 10n different numbers. Binary numbers—numbers base 2—work similarly. A binary number is represented by a sequence of digits each of which is either 0 or 1. These digits are often called bits. The rightmost digit is the 20 place, the next digit towards the left the 21 place, etc.
How many different numbers can be represented by a sequence of length n? 2n. Finger exercise: What is the decimal equivalent of the binary number 10011? 29 30 Chapter 3. Some Simple Numerical Programs Perhaps because most people have ten fingers, we seem to like to use decimals to represent numbers. On the other hand, all modern computer systems represent numbers in binary. This is not because computers are born with two fingers. , devices that can be in only one of two states, on or off. That the computer uses a binary representation and people a decimal representation can lead to occasional cognitive dissonance.
Introduction to Computation and Programming Using Python, Revided & Expanded by John V. Guttag