Search results for "math"

APEX PreCalculus

Contributors: Chapman, Herald, and Libertini

Publisher: APEX Calculus

License: CC BY-NC

This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.

(1 review)

Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)

Contributor: Poritz

Publisher: Jonathan Poritz

License: CC BY-SA

This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.

(1 review)

Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics

Contributor: Poritz

Publisher: Colorado State University Pueblo

License: CC BY-SA

This is a first draft of a free (as in speech, not as in beer, [Sta02]) (although it is free as in beer as well) textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.

(2 reviews)

Open Resources for Community College Algebra

Contributor: Faculty

Publisher: Portland Community College

License: CC BY

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

(4 reviews)

Delftse Foundations of Computation - 2nd Edition

Contributors: Hugtenburg and Yorke-Smith

Publisher: TU Delft Open

License: CC BY-NC-SA

DELFTSE FOUNDATIONS OF COMPUTATION is a textbook for a one-quarter introductory course in theoretical computer science. It includes top-ics from propositional and predicate logic, proof techniques, discrete structures, set theory and the theory of computation, along with practical applications to computer science. It has no prerequisites other than a general familiarity with computer programming.

(1 review)

Mechanics and Relativity

Contributor: Idema

Publisher: TU Delft Open

License: CC BY-NC-SA

In Mechanics and Relativity, the reader is taken on a tour through time and space. Starting from the basic axioms formulated by Newton and Einstein, the theory of motion at both the everyday and the highly relativistic level is developed without the need of prior knowledge. The relevant mathematics is provided in an appendix. The text contains various worked examples and a large number of original problems to help the reader develop an intuition for the physics. Applications covered in the book span a wide range of physical phenomena, including rocket motion, spinning tennis rackets and high-energy particle collisions.

(1 review)

Think Data Structures: Algorithms and Information Retrieval in Java

Contributor: Downey

Publisher: Green Tea Press

License: CC BY-NC-SA

Data structures and algorithms are among the most important inventions of the last 50 years, and they are fundamental tools software engineers need to know. But in my opinion, most of the books on these topics are too theoretical, too big, and too bottom-up:

(3 reviews)

How to Think Like a Computer Scientist: C Version

Contributors: Downey and Scheffler

Publisher: Green Tea Press

License: CC BY-NC

The goal of this book is to teach you to think like a computer scientist. I like the way computer scientists think because they combine some of the best features of Mathematics, Engineering, and Natural Science. Like mathematicians, computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating trade offs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.The single most important skill for a computer scientist is problem-solving. By that I mean the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. That’s why this chapter is called “The way of the program.”

(2 reviews)

How to Think Like a Computer Scientist: C++ Version

Contributor: Downey

Publisher: Green Tea Press

License: CC BY-NC

The goal of this book is to teach you to think like a computer scientist. I like the way computer scientists think because they combine some of the best features of Mathematics, Engineering, and Natural Science. Like mathematicians,computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating trade offs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.The single most important skill for a computer scientist is problem-solving. By that I mean the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. That’s why this chapter is called “The way of the program.”

(1 review)

Object-Oriented Reengineering Patterns

Contributors: Demeyer, Ducasse, and Nierstrasz

Publisher: Stéphane Ducasse

License: CC BY-SA

The documentation is missing or obsolete, and the original developers have departed. Your team has limited understanding of the system, and unit tests are missing for many, if not all, of the components. When you fix a bug in one place, another bug pops up somewhere else in the system. Long rebuild times make any change difficult. All of these are signs of software that is close to the breaking point.

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(0 reviews)