This lab is generally the first lab for this course. It introduces students to desmos.com and helps them become familiar with it.
The lab investigates the visual changes to a line as the slope and y-intercept change.
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.Attribution: This work "Algebra and Trigonometry, 2e" by Jay Abramson is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.
Short Description:
Note: This OpenStax book was imported into Pressbooks on August 7, 2019, to make it easier for instructors to edit, build upon, and remix the content. The OpenStax import process isn't perfect, so there are a number of formatting errors in the book that need attention. As such, we don't recommend you use this book in the classroom. This also means that, while the original version of this book is accessible, this Pressbooks copy is not. For information about how to get your own copy of this book to work on, see the Add Content part in the Pressbooks Guide. You can access the original version of this textbook here: Algebra and Trigonometry: OpenStax.
Long Description:
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
Word Count: 374323
ISBN: 978-1-947172-10-4
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
This course covers the applications of algebra to combinatorics. Topics include enumeration methods, permutations, partitions, partially ordered sets and lattices, Young tableaux, graph theory, matrix tree theorem, electrical networks, convex polytopes, and more.
This book aims to be an accessible introduction into the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them.
The topics covered include:
The divide and conquer technique.
The use of randomization in algorithms.
The general, but typically inefficient, backtracking technique.
Dynamic programming as an efficient optimization for some backtracking algorithms.
Greedy algorithms as an optimization of other kinds of backtracking algorithms.
Hill-climbing techniques, including network flow.
The goal of the book is to show you how you can methodically apply different techniques to your own algorithms to make them more efficient. While this book mostly highlights general techniques, some well-known algorithms are also looked at in depth. This book is written so it can be read from "cover to cover" in the length of a semester, where sections marked with a * may be skipped.
This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.
This problem illustrates how numerical theories are developed, how we might test this theory with an analog model, and how numerical models are constructed and the limitations of numerical modeling.
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.
This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.
Word Count: 15331
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
Comparative planetary geology requires understanding how geological processes are affected by changes in physical environment-each planet and moon provides an opportunity to refine our understanding of how physical geological processes operate. Volcanism is a great example of a major geological process highly susceptible to such variations. Students performing this exercise will constrain how "Amboy Crater" would look if the same eruption happened on the Moon and Mars. Part 1 of the exercise asks small groups to assess either the yield strength of the Amboy flows or the time required for the flow to travel a given distance. After discussion of the results, Part 2 asks students to characterize the dimensions of the same flow, if emplaced on Mars or the Moon (changing only gravitational acceleration), and the time required for it to form; they are asked to predict the outcome in advance. Part 3 uses "Erupt" freeware by Ken Wohletz to explore how gravity changes will affect cinder cone geometry; the model is tested first to see if it correctly predicts an Amboy-like geometry, and afterwards students are asked to brainstorm what other factors should also be modified to improve the accuracy of the simulation, and how these changes would be expected to affect the geomorphological outcome. Finally, Part 4 asks students to use simple ballistic equations, implemented via an online Applet (Stromboli), to constrain the launch angle and starting velocity for the eruption that formed Amboy Crater (modifications are supposedly underway to permit this applet to run with different values of gravitational acceleration and air resistance).
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This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.
A student activity to determine the angle of repose and what factors determine the angle of repose.
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During this exercise, students compare a series of satellite images taken 3-4 years apart to investigate the effects of human land use and annotate the images using ImageJ software.
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Esta guía práctica acompaña la serie de videos Poder estadístico y tamaño de muestra en R, de mi canal de YouTube Investigación Abierta, que recomiendo ver antes de leer este documento. Contiene una explicación general del análisis de poder estadístico y cálculo de tamaño de muestra, centrándose en el procedimiento para realizar análisis de poder y tamaños de muestra en jamovi y particularmente en R, usando los paquetes pwr (para diseños sencillos) y Superpower (para diseños factoriales más complejos). La sección dedicada a pwr está ampliamente basada en este video de Daniel S. Quintana (2019).
We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.
In this problem set students are given Rb/Sr and 87Sr/86Sr data for whole rock and mineral samples from three granitic intrusions in the Sierra Nevada. They use these data (in EXCEL) to calculate isochron ages and initial ages for the intrusions and then interpret their results. This problem is intended to teach some spreadsheet skills (linear regressions, graphing) as well as having them think about the use of radiogenic isotopes.
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This lab exercise provides students with activities utilizing vector operations within the context of the atmospheric and oceanic environments.
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An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text.