# Mathematics - Applied

## Quantitative Problem Solving in Natural Resources

Peter L. Moore, Iowa State University

This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and professional internships.

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## Statistical Thinking for the 21st Century

Russell A. Poldrack, Stanford University

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

(1 review)

## Geometry with an Introduction to Cosmic Topology

Michael P. Hitchman, Linfield College

Motivated by questions in cosmology, the open-content text *Geometry with an Introduction to Cosmic Topology* uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

(1 review)

## Answering questions with data: Introductory Statistics for Psychology Students

Matthew J. C. Crump

This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.

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## First Semester in Numerical Analysis with Julia

Giray Ökten, Florida State University

First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.

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## Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)

Jonathan A. Poritz

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)

## Business Math: A Step-by-Step Handbook

Jean-Paul Olivier

Business math is the study of mathematics required by the field of business. Business professionals will work with taxes, gross earnings, product prices, and currency exchange; they will be offered loans, lines of credit, mortgages, leases, savings bonds, and other financial tools. This textbook covers all of these topics and how these financial tools can maximize their earnings and minimize their costs. It also discusses how to execute smart monetary decisions both personally and for their business.

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## Learning Statistics with R: A tutorial for psychology students and other beginners

Danielle Navarro, University of New South Wales

*Learning Statistics with R* covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.

(1 review)

## Introductory Statistics with Randomization and Simulation First Edition

David Diez, Google/YouTube

Christopher Barr, Varadero Capital

Mine Çetinkaya-Rundel, Duke University

We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods.

(3 reviews)

## Advanced High School Statistics, 2nd Edition

David Diez, OpenIntro

Christopher Barr, Varadero Capital

Mine Çetinkaya-Rundel, Duke University

Leah Dorazio, San Francisco University High School

We hope readers will take away three ideas from this book in addition to forming a foundation

(1 review)