László Tisza was Professor of Physics Emeritus at MIT, where he began …
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.
Use your knowledge of rectangle areas to calculate the missing measurement of …
Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams. Find the value of the question marks in the diagrams. All of the shapes are rectangles but are not drawn to scale.
Build rectangles of various sizes and relate multiplication to area. Discover new …
Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!
Build rectangles of various sizes and relate multiplication to area. Discover new …
Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying large numbers. Use the game screen to test your problem solving strategies!
Arithmetic | Algebra provides a customized open-source textbook for the math developmental …
Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE).
Arithmetic | Algebra Homework book is a static version of the WeBWork …
Arithmetic | Algebra Homework book is a static version of the WeBWork online homework assignments that accompany the textbook Arithmetic | Algebra for the developmental math courses MAT 0630 and MAT 0650 at New York City College of Technology, CUNY.
The purpose of this learning video is to show students how to …
The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.
The subject of enumerative combinatorics deals with counting the number of elements …
The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.
This is a challenge based activity in which students use augmented reality …
This is a challenge based activity in which students use augmented reality and trial and error in order to determine how changes to a quadratic equation affect the shape of a parabola. Students use the Geogebra AR app to manipulate equations and change the parabola to fit around a physical object.
This is a challenge based activity in which students use augmented reality …
This is a challenge based activity in which students use augmented reality and trial and error in order to determine how changes to a quadratic equation affect the shape of a parabola. Students use the Geogebra AR app to manipulate equations and change the parabola to fit around a physical object.
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