Products related to Theorems:
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Godel's Incompleteness Theorems
This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a.It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises.It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H.Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g.Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued.It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature.
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Problems and Theorems in Linear Algebra
There are a number of very good books available on linear algebra.From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones.However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results.Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks.In addition, more than a few interesting old results are not covered in many books.In this book, Prasolov provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs.The book features about 230 problems with complete solutions.It would be a fine supplementary text for an undergraduate or graduate algebra course.
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Journey through Genius : Great Theorems of Mathematics
Praise for William Dunham s Journey Through Genius The GreatTheorems of Mathematics "Dunham deftly guides the reader throughthe verbal and logical intricacies of major mathematical questionsand proofs, conveying a splendid sense of how the greatestmathematicians from ancient to modern times presented theirarguments." Ivars Peterson Author, The Mathematical TouristMathematics and Physics Editor, Science News "It is mathematics presented as a series of works of art; afascinating lingering over individual examples of ingenuity andinsight.It is mathematics by lightning flash." Isaac Asimov "It is a captivating collection of essays of major mathematicalachievements brought to life by the personal and historicalanecdotes which the author has skillfully woven into the text.Thisis a book which should find its place on the bookshelf of anyoneinterested in science and the scientists who create it." R.L.Graham, AT&T Bell Laboratories "Come on a time-machine tour through 2,300 years in which Dunhamdrops in on some of the greatest mathematicians in history.Almostas if we chat over tea and crumpets, we get to know them and theirideas ideas that ring with eternity and that offer glimpses intothe often veiled beauty of mathematics and logic. And all the whilewe marvel, hoping that the tour will not stop." Jearl Walker,Physics Department, Cleveland State University Author of The FlyingCircus of Physics
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Wigner-Type Theorems for Hilbert Grassmannians
Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics.The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics.At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results.Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications.An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.
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What are congruence theorems?
Congruence theorems are a set of rules in geometry that determine when two geometric figures are congruent, meaning they have the same size and shape. These theorems are used to prove that two triangles or other shapes are congruent by showing that their corresponding sides and angles are equal. Some common congruence theorems include the Side-Side-Side (SSS) theorem, Side-Angle-Side (SAS) theorem, Angle-Side-Angle (ASA) theorem, and Angle-Angle-Side (AAS) theorem.
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How do you prove geometric theorems?
To prove geometric theorems, one typically uses deductive reasoning based on established postulates, definitions, and previously proven theorems. The proof usually involves a series of logical steps that demonstrate why the theorem is true. This can include using properties of shapes, angles, lines, and other geometric concepts to show that the statement holds true in all cases. Diagrams are often used to visually represent the geometric relationships being discussed and to help illustrate the steps of the proof.
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What are proportionality theorems in math?
Proportionality theorems in math are a set of rules that describe the relationship between the sides of similar triangles. The most common proportionality theorem is the Side-Splitter Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. Another important proportionality theorem is the Angle Bisector Theorem, which states that if an angle bisector of a triangle intersects the opposite side, it divides that side into segments proportional to the other two sides. These theorems are used to solve problems involving similar triangles and proportions.
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How do proportionality theorems work in mathematics?
Proportionality theorems in mathematics, such as the Side-Splitter Theorem and the Angle Bisector Theorem, establish relationships between the sides and angles of similar triangles. These theorems allow us to make conclusions about the corresponding sides and angles of similar triangles, based on their proportional relationships. By using these theorems, we can solve for unknown side lengths or angles in similar triangles, and also prove that certain lines are parallel or that certain triangles are similar. Overall, proportionality theorems provide a powerful tool for analyzing and solving problems involving similar triangles.
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Journey through Genius: Great Theorems of Mathematics
Journey through Genius: Great Theorems of Mathematics
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Calculus On Manifolds : A Modern Approach To Classical Theorems Of Advanced Calculus
This little book is especially concerned with those portions of ?advanced calculus? in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.The approach taken here uses elementary versions of modern methods found in sophisticated mathematics.The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers).Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
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Foundations of Quantitative Finance, Book VI: Densities, Transformed Distributions, and Limit Theorems
Every finance professional wants and needs a competitive edge.A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it.Many are not—and that is the competitive edge these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books develops the advanced topics in mathematics that finance professionals need to advance their careers.These books expand the theory most do not learn in graduate finance programs, or in most financial mathematics undergraduate and graduate courses. As an investment executive and authoritative instructor, Robert R.Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial services industry and two decades in academia where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the earlier books in the set.While the set offers a continuous progression through these topics, each title can be studied independently. FeaturesExtensively referenced to materials from earlier booksPresents the theory needed to support advanced applicationsSupplements previous training in mathematics, with more detailed developmentsBuilt from the author's five decades of experience in industry, research, and teachingPublished and forthcoming titles in the Robert R.Reitano Quantitative Finance Series:Book I: Measure Spaces and Measurable FunctionsBook II: Probability Spaces and Random VariablesBook III: The Integrals of Riemann, Lebesgue and (Riemann-)StieltjesBook IV: Distribution Functions and ExpectationsBook V: General Measure and Integration TheoryBook VI: Densities, Transformed Distributions, and Limit TheoremsBook VII: Brownian Motion and Other Stochastic ProcessesBook VIII: Itô Integration and Stochastic Calculus 1Book IX: Stochastic Calculus 2 and Stochastic Differential EquationsBook X: Classical Models and Applications in Finance
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Controlling High Blood Pressure through Nutrition, Nutritional Supplements, Lifestyle, and Drugs
Controlling High Blood Pressure through Nutrition, Nutritional Supplements, Lifestyle, and Drugs helps prevent and treat high blood pressure and hypertension, the most common primary diagnosis in the United States and a leading cause of heart attack, heart failure, kidney failure, and stroke. Written by two leading experts in nutrition and hypertension, it takes an integrative and evidence-based approach based on scientific research and clinical studies.It explains what causes high blood pressure and includes easy-to-follow solutions for patients that help to treat and prevent it.These include:The ideal drugs to reduce blood pressure with fewest side effects and optimal efficacyA nutrition program to reduce weight and lower the risk of a cardiovascular problemA comprehensive review of nutritional supplements to improve blood pressure control and reduce cardiovascular diseaseA review of lifestyle changes to improve blood pressure such as a detailed exercise program. This book is for doctors, nutritionists, naturopaths, pharmacists and other health practitioners as well as anyone with a family history of hypertension or overt blood pressure issues that would like to make better and healthier lifestyle choices.
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What are the theorems of Thales' theorem?
Thales' theorem states that if A, B, and C are points on a circle where the line AC is a diameter, then the angle at B is a right angle. Another theorem of Thales is that if two triangles are inscribed in the same circle and share a common side that is a diameter of the circle, then the two triangles are right triangles. These theorems are fundamental in understanding the properties of circles and triangles in geometry.
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Is this solution correct for congruence theorems?
Without knowing the specific solution or congruence theorems in question, it is difficult to determine if the solution is correct. Congruence theorems in geometry are used to prove that two triangles or other shapes are congruent based on certain criteria such as side-side-side, angle-side-angle, etc. To determine if a solution is correct, one would need to carefully check that all the given information and reasoning align with the specific congruence theorem being applied. It is important to verify that all the conditions for congruence are met before concluding that the solution is correct.
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What are the addition theorems used for?
Addition theorems are used in mathematics to simplify and manipulate expressions involving trigonometric functions. They are particularly useful in solving problems related to geometry, physics, and engineering. By using addition theorems, we can express complex trigonometric functions in terms of simpler ones, making it easier to solve equations and analyze relationships between angles and sides in various contexts. Overall, addition theorems help us understand and work with trigonometric functions more effectively.
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What are the addition theorems in trigonometry?
The addition theorems in trigonometry are formulas that express the trigonometric functions of the sum or difference of two angles in terms of the trigonometric functions of the individual angles. The addition theorems for sine, cosine, and tangent are used to simplify trigonometric expressions and solve trigonometric equations. These theorems are important in various fields such as physics, engineering, and mathematics, as they allow for the manipulation and simplification of trigonometric expressions.
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