This course is an introduction to differential geometry. The course itself is …

This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

This text is intended for a brief introductory course in plane geometry. …

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 theorem-proving 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 odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out 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.

This is a reviewed and visually enhanced version of Henry Africk's Elementary …

This is a reviewed and visually enhanced version of Henry Africk's Elementary College Geometry book. 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.

"Euclid's 'Elements' Redux" is an open textbook on mathematical logic and geometry …

"Euclid's 'Elements' Redux" is an open textbook on mathematical logic and geometry based on Euclid's "Elements" for use in grades 7-12 and in undergraduate college courses on proof writing.

Many problem solvers throughout history wrestled with Euclid as part of their early education including Copernicus, Kepler, Galileo, Sir Isaac Newton, Ada Lovelace, Abraham Lincoln, Bertrand Russell, and Albert Einstein. This edition is part of an effort to ensure that tomorrow's great thinkers will have that same privilege.

This is an advanced undergraduate course dealing with calculus in one complex …

This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.

In the first part of this video, we review the idea of …

In the first part of this video, we review the idea of flat space and the Pythagorean theorem. The second part of the video reviews ideas from trigonometry including the unit circle, sine, cosine, and pi. We conclude with a proof of an angle-sum identity.

Geometry is concerned with the various aspects of size, shape and space. …

Geometry is concerned with the various aspects of size, shape and space. In this unit, you will explore the concepts of angles, shapes, symmetry, area and volume through interactive activities.

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction …

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

This course introduces students to selected aspects of geometry and topology, using …

This course introduces students to selected aspects of geometry and topology, using concepts that can be visualized easily. We mix geometric topics (such as hyperbolic geometry or billiards) and more topological ones (such as loops in the plane). The course is suitable for students with no prior exposure to differential geometry or topology. Think of it as a moderate hike, overlooking various parts of the geometry and topology landscape. Bits are flat, bits are uphill, there are occasional rocky parts (may be different for everyone), but none that are designed to be cliff faces. The class moves from one topic to the next quickly, so it’s important to learn continuously.

This course is an introduction to arithmetic geometry, a subject that lies …

This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry.

This course introduces topology, covering topics fundamental to modern analysis and geometry. …

This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.

A Google Drive folder created by Kevin Fink of materials for Math …

A Google Drive folder created by Kevin Fink of materials for Math 2231 - Calculus with Analytical Geometry at the College of DuPage. This is intended to be a foundation for anyone wanting to teach Math 2231 where students would need to spend little to no money for materials during the semester. Includes links to a textbook on openstax, a myopenmath shell template, links to lecture videos, supplemental homework assignments and answers, and the materials for an Area project about approximating area under curves.This resource will be updated as needed. For the google drive folder and the most recent version, visit: https://drive.google.com/drive/folders/1KhhTIXOT2a0oEX1hqMIhDsNi4DaO6NSk?usp=sharing

This interactive textbook includes practice problems, examples, and chapters that range from …

This interactive textbook includes practice problems, examples, and chapters that range from calculating angles and probability to annuities and applying geometry. The content in this e-text was developed using a variety of open educational resources, that were remixed to fit a math applications course in higher education.

In this unit you will see first how to convert vectors from …

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section_2, in which you will also work with bearings.

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