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e-book
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) 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 [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Textbooks
- Resource Type:
- e-book
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e-book
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. 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.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
- Resource Type:
- e-book
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e-book
Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Textbooks Statistics -- Computer programs
- Resource Type:
- e-book
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Video
Masterpieces of microengineering, kinesins are motorized transport machines that move cellular materials to their correct locations in the cell so they can perform their functions. Kinesins have two feet, or "globular heads," that literally walk, one foot over another. Known as the "workhorses of the cell," kinesins can carry cargo many times their own size.
- Course related:
- ABCT2103 Cell Biology
- Subjects:
- Biology
- Keywords:
- Kinesin
- Resource Type:
- Video
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Video
Physicist Werner Heisenberg said, "When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first." As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks. Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work.
- Subjects:
- Physics
- Keywords:
- Turbulence Starry night (Gogh Vincent van)
- Resource Type:
- Video
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Video
Finding the right mate is no cakewalk -- but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics Online dating
- Resource Type:
- Video
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Video
On March 17, 2014, a group of physicists announced a thrilling discovery: the “smoking gun” data for the idea of an inflationary universe, a clue to the Big Bang. For non-physicists, what does it mean? TED asked Allan Adams to briefly explain the results, in this improvised talk illustrated by Randall Munroe of xkcd.
- Subjects:
- Physics and Cosmology and Astronomy
- Keywords:
- Inflationary universe Gravitational waves
- Resource Type:
- Video
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Video
In this lecture, we consider strategies for adversarial games such as chess. We discuss the minimax algorithm, and how alpha-beta pruning improves its efficiency. We then examine progressive deepening, which ensures that some answer is always available.
- Course related:
- COMP4431 Artificial Intelligence
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Artificial intelligence
- Resource Type:
- Video
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e-book
Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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Video
This video playlist covers the topic of: 1. PDE 1 | Introduction 2.PDE 2 | Three fundamental examples 3.PDE 3 | Transport equation: derivation 4.PDE 4 | Transport equation: general solution 5. PDE 5 | Method of characteristics 6. PDE 6 | Transport with decay and nonlinear transport 7.PDE 7 | Wave equation: intuition 8.PDE 8 | Wave equation: derivation 9.PDE 9 | Wave equation: general solution 10.PDE 10 | Wave equation: d'Alembert's formula 11.PDE 11 | Wave equation: d'Alembert examples 12.PDE 12 | Wave equation: characteristics 13.PDE 13 | Wave equation: separation of variables 14.FA 1 | Fourier series introduction 15.FA 2 | Computing Fourier series 16.PDE | Heat equation: intuition 17.PDE | Finite differences: introduction
- Course related:
- AMA3723 Further Mathematical Methods for Finance
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations Partial
- Resource Type:
- Video
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