Advances in Discrete Differential Geometry
Mathematics
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen
Alexander I. Bobenko
https://link.springer.com/content/pdf/10.1007%2F9783662504475.pdf
Springer
2016
Baihaqi
Creative Commons
PDF
English
Textbooks
Introduction to Louis Michel’s lattice geometry through group action
geometry
This chapter describes the outline of the book and explains the interrelations between different chapters and appendices. The specificity of this book is an intensive use of group action ideas and terminology when discussing physical and mathematical models of lattices. Another important aspect is the discussion and comparison of various approaches to the characterization of lattices. Along with symmetry and topology ideas, the combinatorial description based on Voronoï and Delone cells is discussed along with classical characterization of lattices via quadratic forms.
B. Zhilinskii
https://www.edpopen.org/images/stories/books/fulldl/Introduction_to_Louis_Michels_lattice.pdf
EDP Sciences
2015
Baihaqi
Creative Commons
PDF
English
Textbooks
Geometry with an Introduction to Cosmic Topology
Geometry, Cosmic Topology
Motivated by questions in cosmology, the opencontent 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.
The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in nonEuclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
Michael P. Hitchman,
https://mphitchman.com/geometry/GCT2018.pdf
Independent
2018
Baihaqi
Creative Commons
PDF
English
Textbooks
Trigonometry
Trigonometry
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.
Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section.
Ted Sundstrom, Steven Schlicker
https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1012&context=books
Grand Valley State University
2016
Baihaqi
Creative Commons
PDF
English
Textbook
College Trigonometry
Trigonometry

Carl Stitz, Jeff Zeager
http://www.stitzzeager.com/szct07042013.pdf
Stitz Zeager Open Source Mathematics
2011
Baihaqi
Creative Comnmons
PDF
English
Textbook
Trigonometry
Trigonometry
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged.
Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior athematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section
Ted Sundstrom, Steven Schlicker
https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1012&context=books
Grand Valley State University
2017
Baihaqi
Creative Commons
PDF
English
Textbook
Trigonometry
Trigonometry
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry  the relationship between angles and distances.
Richard Beveridge
https://open.umn.edu
Independent
2014
Baihaqi
Creative Commons
PDF
English
Textbook
Fast Fourier Transforms
Transforms
Mathematics
This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting.
C. Sidney Burrus
Matteo Frigo
Steven G. Johnson
Markus Pueschel
Ivan Selesnick
Connexions
Cut Rita Zahara
Creative Commons
Textbooks
Elementary College Geometry
Geometry
Mathematics
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.
The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theoremproving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.
The problems are arranged in pairs so that just the oddnumbered or just the evennumbered can be assigned. For assistance, the student may refer to a large number of completely workedout examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.
This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
Henry Africk
CUNY Academic Works
Cut Rita Zahara
Creative Commons
Textbooks
Geometry
Geometry
Mathematics
Geometry is used in many areas—from art to science. For example, geometry plays a key role in construction, fashion design, architecture, and computer graphics. This course focuses on the main ideas of geometry that are the foundation of applications of geometry used everywhere. In this chapter, you’ll study the basic elements of geometry. Later you will prove things about geometric shapes using the vocabulary and ideas in this chapter—so make sure that you completely understand each of the concepts presented here before moving on.
Victor Cifarelli
Andrew Gloag
Dan Greenberg
Jim Sconyers
Bill Zahner
CK12 Foundation
Cut Rita Zahara
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