This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

    CONGRATULATIONS TO HERBERT KROEMER, 2000 NOBEL LAUREATE FOR PHYSICS For upper-division courses in thermodynamics or statistical mechanics, Kittel and Kroemer offers a modern approach to thermal physics that is based on the idea that all physical systems can be described in terms of their discrete quantum states, rather than drawing on 19th-century classical mechanics concepts.

    Who ever heard of a peasant marrying a princess? But Pong Lo is wiser than the Emperor knows. And when he concocts a potion that saves the Princess's life, the Emperor gladly offers him any reward he chooses--except the Princess.   Pong Lo makes a surprising request. He asks for a single grain of rice, doubled every day for one hundred days. The baffled Emperor obliges--only to discover that if you're as clever as Pong Lo, you can turn a single grain of rice into all the wealth and happiness in the world! Praise for A Grain of Rice: "Clever and quietly told in simple, yet evocative language."-Kirkus Reviews"Pittman invites readers into her story through her choice of concrete objects, sensory images, and universal messages. She borrows from the motifs of oral literature, and also weaves in information about arithmetical progression and 15th-Century Chinese people, patterns, and traditions. Pittman's well executed pencil drawings ooze with emotion, and there is a fusion of text and illustrations...[A] book that is wise and humorous, and one to be perused and savored."-School Library Journal"Gracefully illustrated with finely shaded drawings, this picture book tells of Pong Lo, a poor Chinese peasant who wins the hand of the emperor's daughter through his knowledge of mathematical principles."-Booklist

    It was written especially for children who have been convinced by the attitudes of adults that mathematics is (1) impossible (2) only for bright kids (3) no fun at all anyway. This book says that maths is nothing more than a way of looking at the world and that it can be relevant to everyday life (Street maths) and fun (How many sides does a banana have?). Hundreds of mathematical events, jokes, riddles, puzzles, investigations and experiments prove it!

    Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

    Whenever they'd get the chance, they'd dance! She'd sing and snap. He'd tappity-tap. What a pair they made! At the end of each day, they'd always say, "ONE, TWO, I'll count on you, 'til the end, we'll be best friends." Until Three jumps in between them . . . Suddenly One only wants to play with Three. "ONE, THREE, odds we'll be!" they chant. Two feels left out. But what can she do? Another character-building counting book by award-winning author Kathryn Otoshi, Two is a powerful story of friendship, loss, letting go, and self-discovery.

    Children's Choice Award winner Bethany Barton applies her signature humor to the scariest subject of all: math!Do multiplication tables give you hives? Do you break out in a sweat when you see more than a few numbers hanging out together? Then I'm Trying to Love Math is for you! In her signature hilarious style, Bethany Barton introduces readers to the things (and people) that use math in amazing ways -- like music, and spacecraft, and even baking cookies! This isn't a how-to math book, it's a way to think differently about math as a necessary and cool part of our lives!

    

    . .Which team deserves the spotlight? Whose talents will steal the scene? Colors can really mix it up, but nobody stacks higher than shapes.Red and his primary pals have some colorful surprises in store. Circle and his crew reveal whole new sides of themselves. How will the judges ever pick a winner?Author-illustrator Mike Boldt delivers a laugh-out-loud talent show that explores both colors and shapes and invites us to appreciate the amazing things that can happen if they come together.

    Kids are encouraged to recognize patterns, which are everywhere -- in the colors of the fish, the backgrounds, the text, and the borders. A note to readers in the back of the book identifies even more patterns to look for!

    The authors present updated coverage of compilers based on research and techniques that have been developed in the field over the past few years. The book provides a thorough introduction to compiler design and covers topics such as context-free grammars, fine state machines, and syntax-directed translation.

    Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

    Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning.The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models.Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

    And watch out for One Finger Jimmy, Chainsaw Charlie and their gangster friends, who are living proof that maths can be murderous.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.