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Precalculus
Thomas Tradler and Holly Carley · CUNY New York City College of Technology
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY. Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use.
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College Algebra
Jay Abramson · Arizona State University
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebraoffers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
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Time Scales Analysis
Svetlin G. Georgiev · Sorbonne University
Time scale theory was first initiated by Stefan Hilger in 1988 in his PhD thesis to unify both approaches of dynamic modelling: difference and differential equations. Similar ideas have been used before and go back in the introduction of the Riemann-Stieltjes integral which unifies sums and integrals. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, tim
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Basic Statistics Using R for Crime Analysis
Jaeyong Choi · West Chester University
This text is for those interested in becoming crime analysts, focusing on learning statistics without delving too deeply into mathematics. Moreover, this book emphasizes practical applications by utilizing R for data analysis, ensuring students can develop relevant skills beyond the university. I hope that students can easily follow the instructions in this book and replicate the same outcomes using the provided data. This practical experience will demonstrate the value of statistics and R.
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Yet Another Introductory Number Theory Textbook - Cryptology Emphasis
Jonathan A. Poritz · Colorado State University – Pueblo
This introductory number theory textbook has a particular emphasis on connections to cryptology. The cryptologic material arising naturally 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 of the purity and eternal inapplicability of number theory.
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Applied Linear Algebra and Differential Equations
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
These lecture notes are for a mathematics course offered to second-year engineering students. Material from our usual courses on linear algebra and differential equations have been combined into a single course (essentially, two half-semester courses) at the request of our Engineering School. I have tried my best to select the most essential and interesting topics from both courses, and to show how knowledge of linear algebra can improve students’ understanding of differential equations.
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Math 091: Essentials of Intermediate Algebra
Patrick Kwon · Highline College
This text addresses intermediate algebra and aims to develop understanding of functions (linear, exponential, and quadratic) as well as proficiency with simplifying expressions involving integer exponents, solving linear inequalities, and solving linear equations in two variables.
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Lebesgue Integration on Time Scales
Svetlin G. Georgiev · Sorbonne University, Paris, France
LibreTexts
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Elementary Trigonometry
Richard W. Beveridge · Clatsop Community College
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.
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Elementary Algebra
LibreTexts · LibreTexts
Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.
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Abstract Algebra I
Pamini Thangarajah · Mount Royal University
Abstract algebra is a fascinating area of study within mathematics that explores the intricacies of algebraic structures such as groups, rings, and fields. These structures are defined using abstract axioms, and the focus is on understanding their properties independently of any specific mathematical objects or physical systems. It is a highly abstract and theoretical field, but one that has practical applications in areas such as computer science, physics, chemistry and engineering.
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College Algebra and Trigonometry
Richard W. Beveridge · Clatsop Community College
This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.
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MAT 1130: Mathematical Ideas
Andy Jones · Prince George's Community College
This OER was created for MAT 1130 Mathematical Ideas at Prince George’s Community College. It presents core quantitative concepts and supports practical reasoning skills across multiple areas of mathematics. It covers foundational topics such as set theory, formal logic, personal finance, probability, descriptive statistics, voting methods and apportionment. The text includes a collection of review exercises for every chapter, reinforcing key ideas and supporting mastery of course outcomes.
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Math 4A: Multivariable Calculus
Zoya Kravets · Mission College
Math 4A: Multivariable Calculus at Mission College is the third and final part of a three-semester calculus sequence for students in math, physics, and engineering majors. The course covers topics such as: Vector-valued functions, Calculus of functions with more than one variable, Partial derivatives, Differentials, Gradients, Lagrange multipliers, Multiple integration, Line integrals, Surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence theorem.
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Advanced Algebra
Anonymous · LibreTexts
Intermediate Algebra is the second part of a two-part course in Algebra that builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of applications found in most disciplines. Used as a standalone textbook, it offers plenty of review as well as something new to engage the student in each chapter. This textbook introduces functions early and stresses the geometry behind the algebra.
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Mathematical Biology
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
Biology, as is usually taught, requires memorizing a wide selection of facts and remembering them for exams, sometimes forgetting them soon after. For students exposed to biology in secondary school, this text may seem like a different subject. The ability to model problems using mathematics requires almost no rote memorization, but it does require a deep understanding of basic principles and a wide range of mathematical techniques.
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MTH 15: Applied Calculus I
LibreTexts
This calculus course is intended for majors in business and in certain areas of life sciences. The course covers differential calculus of algebraic, exponential, and logarithmic functions, introduction to integral calculus, and applications in business, economics, and the life and social sciences.
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The Laplace and Fourier Transforms on Time Scales
Svetlin G. Georgiev · Sorbonne University, Paris, France
Time scale theory was first initiated by Stefan Hilger in 1988 in his PhD thesis to unify both approaches of dynamic modelling: difference and differential equations. Similar ideas have been used before and go back in the introduction of the Riemann-Stieltjes integral which unifies sums and integrals. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, tim
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Math in Society
David Lippman · Pierce College
This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics.
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Las matemáticas de la inteligencia artificial
Joaquin López Herraiz · Universidad Complutense de Madrid
El objetivo de este libro es mostrar la conexión existente entre los fundamentos de la inteligencia artificial y los contenidos de asignaturas como Cálculo Multivariable y Cálculo Diferencial de los grados de Física y Matemáticas.