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Math C180: Calculus I
Chau D Tran · Coastline College
This is the first course in the calculus sequence. It satisfies the requirement for majors in mathematics, science, or engineering. Topics include limits, derivatives of algebraic and transcendental functions, applications of derivatives, indefinite integrals, definite integrals, the Fundamental Theorem of Calculus, and applications of integration.
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Linear Algebra
David Cherney, Tom Denton, & Andrew Waldron · University of California, Davis
Linear algebra is the study of vectors and linear transformations. This text is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.
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Introduction to Mathematical Analysis I
Lafferriere, Lafferriere, and Nguyen · LibreTexts
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
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A Primer of Real Analysis
Dan Sloughter · Furman University
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
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Applied Geometric Algebra (Tisza)
László Tisza · Massachusetts Institute of Technology
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools.
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Introduction to Groups and Geometries
David W. Lyons · Lebanon Valley College
This text is two textbooks in one: an introduction to group theory, and an introduction to modern geometries using the Kleinian paradigm. The book can be used for a combined one-semester course in both subjects, or, through supplementary projects, it can be used for a one-semester introduction to group theory or a one-semester introduction to modern geometries.
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Informal Calculus with Applications to Biological and Environmental Sciences
Tyler Seacrest · University of Montana Western
This book is an approachable introduction to calculus with applications to biology and environmental science. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.
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Acoustics
Wikipedia · LibreTexts
Acoustics is the science that studies sound, in particular its production, transmission, and effects. The science of acoustics has many applications which are dependent upon the nature of the sound that is to be produced, transmitted or controlled. In the case of a desirable sound, such as music, the main application of acoustics is to make the music sound as good as possible.
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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.