Word Count: 15331
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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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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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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.
Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.
In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked.
The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.
To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.
Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.
The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.
Best open source book in Discrete Math. Covers all the subjects in a standard Discrete Math class for mathematics or computer science students and contains sage cells for all subjects. Set Theory, Combinatorics, Logic, Relations, Recursion, Graph Theory, Trees, Algebraic Structures, Boolean Algebras, Automata, etc. Originally published commercially, its original text was peer-reviewed and was adopted for use at several universities throughout the country. Now in its open source version, has the same quality but it is free.
László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976.
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 sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.
This applied mathematics textbook covers Matrices and Pathways, Statistics and Probability, Finance, Cyclic, Recursive and Fractal Patterns, Vectors, and Design. The approach used is primarily data driven, using numerical and geometrical problem-solving techniques.
Applied Mathematics, Third Edition. This textbook was written for the math component for Associate of Applied Science degrees at the College of Southern Nevada.
NSCC MATH 1020
Short Description:
Applied Math for Food Service is an adapted open textbook created by Amy Savoury. This new open textbook remixes content from two open textbooks published by BC Campus under CC BY licences: Basic Kitchen & Food Service Management by The BC Cook Articulation Committee, and Math for Trades by Chad Flinn and Mark Overgaard.
Word Count: 26676
ISBN: 978-1-990641-68-8
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I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; well learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options.
Applied Technical Mathematics for Horticulture and Diesel Mechanics is intended for a one-semester class with students who enter the semester with a good working-level of math skills. High school algebra and geometry are the only prerequisites,The technical math course at Kishwaukee College is unique in that the class combines students in horticulture with those from diesel mechanics. The course materials apply to both areas, as much as possible. The intent is to provide a solid foundation for solving job-related math problems for all students in the class. For this reason, the focus is on "how to solve" more than "why does this work?"Feedback, comments, etc. would be greatly appreciated!Robert E. Brownrbrown3@kish.edu
A series of 6 Excel-based projects on the mathematics of biodiversity for basic college math classes and developmental math classes. Students learn about the structure of biodiversity, the application of many basic data analysis skills, and the use of Excel for analysis and data presentation.
This Project has been completed as part of a standard 10 weeks Calculus 3 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.