Home
Search results “Number theory analysis and geometry”
Strategic Research to Solve Conjectures in Arithmetic Geometry
 
04:27
The KiPAS Arithmetic Geometry and Number Theory Group is researching various conjectues concerning special values of L-functions, especially by using a geometric object called the polylog. “Algebraic varieties are geometric objects given as the zeros of polynomials. Various conjectures exist regarding special values of L-functions for such algebraic varieties. Our primary objective is to explore such conjectures.” All positive integers can be uniquely expressed as a product of prime numbers. Prime numbers are like the “atoms” constituting an integer with respect to the product, and the properties of prime numbers are captured by L-functions. The simplest example of an L-function is a function called the Riemann zeta function, which is expressed by this type of infinite sum with respect to a real numbers that are greater than 1. This infinite sum can be re-expressed as an infinite product parameterized by prime numbers. “Since the time of Euclid, it has been known that there are an infinite number of prime. It was discovered by Euler that this fact corresponds to the analytic fact that the Riemann zeta function diverges when the variable s approaches 1. This type of phenomenon is now being researched in even greater depth.” Important invariants in number theory and special values of L-function are of totally different worlds, so that it is surprising to expect a connection. The idea behind arithmetic geometry is to introduce geometric objects in order to make a connection between the two. The KiPAS Arithmetic Geometry and Number Theory Group is focused on a geometric object called the “polylog”. “Arithmetic conjectures of L-functions try to connect two entirely different quantities of algebraic varieties, namely special values of L-functions which are analytic, and arithmetic information of the algebraic variety. One method to achieve this goal is to introduce a certain geometric object that intrinsically contains both quantities. One simple example of a geometric is a polygon, which intrinsically contains quantities such as the number of vertices and the number of sides. For our conjecture, the polylog is an extremely promising but complicated geometric object. Grothendieck refers to this type of geometrical object as a “motif”. Motif is a word that originates in the description of the work of Cézanne, and it has the same type of connotation as a motif of an artwork. If important but seemingly very different invariants can be interpreted as intrinsic features of a common motif, then one may be able to deduce relation between the different invariants.” The members of the KiPAS Arithmetic Geometry and Number Theory Group are conducting research as a team, and by studying the polylog, the team is endeavoring to solve important conjectures in arithmetic geometry.
Complex Analysis  and algebraic geometry
 
18:57
In many ways, the modern revival of algebraic geometry resulted from investigations in complex function theory. In this video, we show how Weierstrass's p-function can be used to relate cubic curves and 2-tori. We see in particular that cubic curves have an abelian group structure. The material in this video and the other in the playlist can be found in Kirwan's "Complex algebraic curves".
Views: 1823 DanielChanMaths
David Nadler. Back in Black: Geometry's Payment Plan to Number Theory
 
36:00
2016 Breakthrough Prize Symposium in Mathematics Session: Mathematical Horizons Chair: David Eisenbud (UC Berkeley) Featuring talks by: 1. Sourav Chatterjee (Stanford). Nonlinear Large Deviations. 2. Lauren Williams (UC Berkeley). Combinatorics of Hopping Particles and Orthogonal Polynomials. 3. Ian Agol (UC Berkeley). Thurston's Vision Fulfilled? 4. David Nadler (UC Berkeley). Back in Black: Geometry's Payment Plan to Number Theory. 5. George Lakoff (UC Berkeley). The Brain's Mathematics: The Cognitive and Neural Foundations of Mathematics. The 2016 Breakthrough Prize Symposium is co-hosted by UC Berkeley, UC San Francisco, Stanford, and the Breakthrough Prize Foundation. This daylong event includes talks and panels featuring Breakthrough Prize laureates in Fundamental Physics, Life Sciences and Mathematics, as well as other distinguished guests. For more details on the day's activities please visit: http://breakthroughprize.berkeley.edu/symposium
Views: 300 UC Berkeley Events
Fundamental Theorem of Algebra - Numberphile
 
15:26
Part one on odd polynomials: http://youtu.be/8l-La9HEUIU More links & stuff in full description below ↓↓↓ A nice extra bit about complex numbers: http://youtu.be/-IJuqR6nz_Q Professor David Eisenbud is an algebraic geometer (and director of the Mathematical Sciences Research Institute at Berkeley) Hello Internet: http://www.hellointernet.fm Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
Views: 909839 Numberphile
The History of Mathematics and Its Applications
 
21:18
Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 ►Courses Offered Through Coursera (Affiliate Links) Logic: https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fmathematical-thinking Graph Theory: https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fgraphs Discrete Math (includes a range of topics meant for computer scientists including graph theory, number theory, cryptography, etc): https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Fspecializations%2Fdiscrete-mathematics Intro to Complex Analysis: https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fcomplex-analysis Game Theory: https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fgame-theory-1 Cryptography: https://click.linksynergy.com/deeplink?id=vFuLtrCrRW4&mid=40328&murl=https%3A%2F%2Fwww.coursera.org%2Flearn%2Fcrypto ►Books (Affiliate Links) Graph Theory: https://amzn.to/2IUXQ0A Logic/Proofs: https://amzn.to/2Cgh2oj Algorithms: https://amzn.to/2Cg0kWg Cryptography: https://amzn.to/2CKIATS Fermat's Last Theorem: https://amzn.to/2yzWNhY Chaos Theory: https://amzn.to/2Cgup83 ►Related Youtube Videos Turning a Sphere Inside Out: https://www.youtube.com/watch?v=-6g3ZcmjJ7k Cutting a Mobius Strip (Visual): https://www.youtube.com/watch?v=XlQOipIVFPk Group Theory Lectures: https://www.youtube.com/watch?v=O4plQ5ppg9c&index=1&list=PLAvgI3H-gclb_Xy7eTIXkkKt3KlV6gk9_ Chaos Theory Lectures: https://www.youtube.com/watch?v=ycJEoqmQvwg&index=1&list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V Geodesics Animation: https://www.youtube.com/watch?v=Wl8--BsbNnA ►Support the Channel Patreon: https://patreon.com/majorprep PayPal(one time donation): https://www.paypal.me/majorprep MajorPrep Merch Store: https://teespring.com/stores/majorprep ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► For more information on math, science, and engineering majors, check us out at https://majorprep.com Best Ways to Contact Me: Facebook, twitter, or email ([email protected])
Views: 32552 MajorPrep
Four Basic Proof Techniques Used in Mathematics
 
22:38
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! A big THANKS to all of those who support me on Patreon! https://www.patreon.com/patrickjmt Part 1: https://youtu.be/KRLBya7x5ZQ Extra Proof by Contradiction with some death intrigue (huh?!) https://www.youtube.com/watch?v=rOGqq1O1rzI&feature=youtu.be New to proving mathematical statements and theorem? I this video I prove the statement 'the sum of two consecutive numbers is odd' using direct proof, proof by contradiction, proof by induction and proof by contrapositive.
Views: 80769 patrickJMT
SummerSchool "Arithmetic geometry" Tschinkel - Introduction | 2006
 
53:39
lecture notes: https://drive.google.com/file/d/1VLucSK53-iLrVUbPAanNZ6Lb7nAAgaQ1/view?usp=sharing Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry" survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Göttingen. Intended for graduate students and recent Ph.D.'s, this volume will introduce readers to modern techniques and outstanding conjectures at the interface of number theory and algebraic geometry. The main focus is rational points on algebraic varieties over non-algebraically closed fields. Do they exist? If not, can this be proven efficiently and algorithmically? When rational points do exist, are they finite in number and can they be found effectively? When there are infinitely many rational points, how are they distributed? For curves, a cohesive theory addressing these questions has emerged in the last few decades. Highlights include Faltings' finiteness theorem and Wiles's proof of Fermat's Last Theorem. Key techniques are drawn from the theory of elliptic curves, including modular curves and parametrizations, Heegner points, and heights. The arithmetic of higher-dimensional varieties is equally rich, offering a complex interplay of techniques including Shimura varieties, the minimal model program, moduli spaces of curves and maps, deformation theory, Galois cohomology, harmonic analysis, and automorphic functions. However, many foundational questions about the structure of rational points remain open, and research tends to focus on properties of specific classes of varieties. Contents About the cover: Rational points on a K3 surface Noam Elkies Curves Rational points on curves Henri Darmon Non-abelian descent and the generalized Fermat equation Hugo Chapdelaine Merel's theorem on the boundedness of the torsion of elliptic curves Marusia Rebolledo Generalized Fermat equations Pierre Charollois Heegner points and Sylvester's conjecture Samit Dasgupta and John Voight Shimura curve computations John Voight Computing Heegner points arising from Shimura curve parametrizations Matthew Greenberg The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points Matthew Greenberg Lectures on modular symbolsLectures on modular symbols Yuri I. Manin Surfaces Rational surfaces over nonclosed fields Brendan Hassett Non-abelian descent David Harari Mordell-Weil Problem for Cubic Surfaces, Numerical Evidence Bogdan Vioreanu Higher-dimensional varieties Algebraic varieties with many rational points Yuri Tschinkel Birational geometry for number theorists Dan Abramovich Arithmetic over function fields Jason Starr Galois + Equidistribution=Manin-Mumford Nicolas Ratazzi and Emmanuel Ullmo The Andre-Oort conjecture for products of modular curves Emmanuel Ullmo and Andrei Yafaev Moduli of abelian varieties and p-divisible groups Ching-Li Chai and Frans Oort Cartier isomorphism and Hodge Theory in the non-commutative case Dmitry Kaledin http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/
Euler's formula with introductory group theory
 
24:28
How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: - Application software engineer: http://3b1b.co/ecl-app-se - Infrastructure engineer: http://3b1b.co/ecl-infra-se - Lab focused engineer: http://3b1b.co/ecl-lab-se - Scientific computing engineer: http://3b1b.co/ecl-sci-comp Special thanks to the following Patrons: http://3b1b.co/epii-thanks There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 776891 3Blue1Brown
Michael Atiyah, From Quantum Physics to Number Theory [2010]
 
01:04:19
Professor Michael Atiyah of the University of Edinburgh, winner of the Fields Medal in 1966 and the Abel Prize in 2004 , on a visit to IMPA gave a lecture titled "From Quantum Physics to Number Theory." Date: December 1, 2010 Video taken from: http://video.impa.br/index.php?page=solenidades-e-palestras-especiais
Views: 9358 Graduate Mathematics
Introduction to Higher Mathematics - Lecture 16:  Group Theory
 
31:59
Now we leave the world of real analysis and explore abstract algebra, beginning with some beautiful structures called groups that will serve to unify mathematics as a whole.
Views: 204826 Bill Shillito
1. Introduction to Poker Theory
 
30:49
MIT 15.S50 Poker Theory and Analysis, IAP 2015 View the complete course: http://ocw.mit.edu/15-S50IAP15 Instructor: Kevin Desmond An overview of the course requirements, expectations, software used for tournaments, advanced techniques, and some basics tools and concepts for the class are discussed in this lecture. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 423352 MIT OpenCourseWare
The Practice of Mathematics - Part 4
 
01:08:24
The Practice of Mathematics Robert P. Langlands Institute for Advanced Study November 16, 1999 Robert P. Langlands, Professor Emeritus, School of Mathematics. There are several central mathematical problems, or complexes of problems, that every mathematician who is eager to acquire some broad competence in the subject would like to understand, even if he has no ambition to attack them all. That would be out of the question! Those with the most intellectual and aesthetic appeal to me are in number theory, classical applied mathematics and mathematical physics. In spite of forty years as a mathematician, I have difficulty describing these problems, even to myself, in a simple, cogent and concise manner that makes it clear what is wanted and why. As a possible, but only partial, remedy I thought I might undertake to explain them to a lay audience. I shall try for a light touch including, in particular, some historical background. Nevertheless the lectures are to be about mathematics. In the first set, there will be geometrical constructions, simple algebraic equations, prime numbers, and perhaps an occasional integral. Every attempt will be made to explain the necessary notions clearly and simply, taking very little for granted except the good will of the audience. Starting in the easiest place for me, I shall give, during the academic year 1999/2000 about eight lectures on pure mathematics and number theory with the motto beautiful lofty things . Beginning with the Pythagorean theorem and the geometric construction of the Pythagorean pentagram, I shall discuss the algebraic analysis of geometric constructions and especially the proof by Gauss in 1796 of the possibility of constructing with ruler and compass the regular heptadecagon. This was a very great intellectual achievement of modern mathematics that can, I believe, be understood by anyone without a great aversion to high-school algebra. Then I will pass on to Galois's notions of mathematical structure, Kummer's ideal numbers, and perhaps even the relations between ideal numbers and the zeta-function of Riemann. This material will be a little more difficult, but I see no reason that it cannot be communicated. It brings us to the very threshold of current research. Since this attempt is an experiment, the structure and nature of the lectures will depend on the response of the audience and on my success in revealing the fabric of mathematics. If it works out, I would like to continue in following years on classical fluid mechanics and turbulence, with motto l'eau mêlée à la lumière , and then, with the somewhat trite motto с того берега, on the analytical problems suggested by renormalization in statistical mechanics and quantum field theory. More videos on http://video.ias.edu
Walter B. Rudin: "Set Theory: An Offspring of Analysis"
 
01:00:01
Prof. Walter B. Rudin presents the lecture, "Set Theory: An Offspring of Analysis." Prof. Jay Beder introduces Prof. Dattatraya J. Patil who introduces Prof. Walter B. Rudin in the second Marden Lecture at UWM.
Riemann Hypothesis - Numberphile
 
17:04
Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis. More links & stuff in full description below ↓↓↓ Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat's Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel's book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley - http://edwardfrenkel.com The Millennium Prize at the Clay Mathematics Institute: http://www.claymath.org Number Line: http://youtu.be/JmyLeESQWGw CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem) Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
Views: 2541659 Numberphile
Pre Regional Mathematical Olympiad 2017 Q.21 to Q.30
 
37:52
Pre Regional Mathematical Olympiad 2017 Q 21 to Q 30 by Maths HOD AGL Sir
Views: 25951 Resonance Eduventures
(Structural Analysis) - Harmonic Density and Graph Theory
 
17:36
The voice is Google Translate :) The Scottish accent, despite its apparent charms in certain parts of the world, is notoriously difficult for the foreigner to understand. For the sake of widening the potential reach of the video, I felt it best not to record myself speaking, but use the Google Translate voice (I imported my script sentence by sentence into Translate, then spliced/edited using basic DAW software. Excuse the occasional odd timing/phrasing due to the Translate voice). Note also that the instrument parts are simply VST's. With this video, it is the theoretical content that is of main importance, hence i'm not too worried about recording string parts on strings, using a real piano etc. The sounds suffice to illustrate the point. I do apologise if the pacing of this video is very slow - i'm always unsure with this type of article as to the pace. I'm assuming those who watch this will probably be musicians (hence keeping the maths very straightforward), hence i've made the video move very slowly and deliberately. I would personally find the video to be better paced if it were at least 3 times the speed of this, but i'm keeping it very slow in the hope that all the concepts will be understood. This is the first of a number of videos I intend to post that will hopefully shed some insight on certain mathematical relationships to sound. This video focuses on the relationship between harmonic density and Graph Theory. Whether this relationship has been stated before i'm unsure of (I simply work on my own projects), but if it hasn't, it should give a new type of insight into texture/density etc. Potentially 'controversial' issue - the definition of a chord - i'm aware of the issues surrounding this. What has to be established is whether the presence of a single interval denotes the presence of a 'chord'. If so, we'd have to class a Bach two-part invention as a 'chordal' work. Of course, how the material is treated also has relevance/significance. Personally, i'd classify a chord as 'the presence of more than one interval at any given temporal instance'. I'm slightly reticent with regards whether to post videos such as this, as the nature of this YouTube channel is a focus on piano music, as opposed to theory. We'll see how this video goes, then i'll take it from there. I'm imagining no more than a handful of views - with at least 2 or 3 of those views being myself checking the upload was successful!! Should there be interest, I intend, over the next while, to post videos on the following subjects: 1) Graph-theoretic dissonance mapping 2) Multitonal graph-theoretic relational mapping 3) 'Big' data - spectral graph theoretic analysis of melodic and harmonic movement (as an aside, I must add a link to Fan Chung's fantastic book on the subject of Spectral Graph Theory - well worth a read - http://www.math.ucsd.edu/~fan/research/revised.html For me, this book is a masterpiece of Mathematics, and Chung is one of the key figures in this field. Plus, she has an Erdos number of 1!!) 4) 'Sacred Geometry' - the Purcell Code 5) Laguerre minimal surfaces/isotropic geometry and its relation to harmonic analysis then a bunch of prime number related work (the majority of my recent compositional output has been prime-based, and the following articles will be in relation to interesting patterns that have emerged as a consequence of this, and research into prime number theory): 1) Integer factorization and RSA - illuminating the semiprime/prime trinity 2) Abandoning the Zeta function 3) Musical cryptography/cryptographic treatment and analysis of sound (much more on this very soon, however) etc Hopefully this video will be self-explanatory. If it doesn't make sense, there are a plethora of videos on the subject on YouTube, and many more very useful articles can easily be found with a simple Google search. All best Kris
Views: 2358 Kris Lennox
Analysis, Spectra, and Number Theory - Discussion Session
 
40:19
December 15, 2014 - Analysis, Spectra, and Number theory: A conference in honor of Peter Sarnak on his 61st birthday. This discussion session opens the conversation up to the audience to discuss current problems in number theory.
Views: 1241 princetonmathematics
Complex Analysis - Fundamental(Lecture1)
 
23:32
Some Basic Fundamentals before starting complex analysis, Unit- I of Engineering Mathematics-III
What is ALGEBRAIC GEOMETRY? What does ALGEBRAIC GEOMETRY mean? ALGEBRAIC GEOMETRY meaning
 
04:23
What is ALGEBRAIC GEOMETRY? What does ALGEBRAIC GEOMETRY mean? ALGEBRAIC GEOMETRY meaning - ALGEBRAIC GEOMETRY definition -ALGEBRAIC GEOMETRY explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like lemniscates, and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the curve and relations between the curves given by different equations. Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique. In the 20th century, algebraic geometry split into several subareas. The mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more generally to the points with coordinates in an algebraically closed field. The study of the points of an algebraic variety with coordinates in the field of the rational numbers or in a number field became arithmetic geometry (or more classically Diophantine geometry), a subfield of algebraic number theory. The study of the real points of an algebraic variety is the subject of real algebraic geometry. A large part of singularity theory is devoted to the singularities of algebraic varieties. With the rise of the computers, a computational algebraic geometry area has emerged, which lies at the intersection of algebraic geometry and computer algebra. It consists essentially in developing algorithms and software for studying and finding the properties of explicitly given algebraic varieties. Much of the development of the mainstream of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on "intrinsic" properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space; this parallels developments in topology, differential and complex geometry. One key achievement of this abstract algebraic geometry is Grothendieck's scheme theory which allows one to use sheaf theory to study algebraic varieties in a way which is very similar to its use in the study of differential and analytic manifolds. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz, with a maximal ideal of the coordinate ring, while the points of the corresponding affine scheme are all prime ideals of this ring. This means that a point of such a scheme may be either a usual point or a subvariety. This approach also enables a unification of the language and the tools of classical algebraic geometry, mainly concerned with complex points, and of algebraic number theory. Wiles's proof of the longstanding conjecture called Fermat's last theorem is an example of the power of this approach.
Views: 1262 The Audiopedia
Imaginary Numbers Are Real [Part 1: Introduction]
 
05:47
More information and resources: http://www.welchlabs.com Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering. Part 1: Introduction Part 2: A Little History Part 3: Cardan's Problem Part 4: Bombelli's Solution Part 5: Numbers are Two Dimensional Part 6: The Complex Plane Part 7: Complex Multiplication Part 8: Math Wizardry Part 9: Closure Part 10: Complex Functions Part 11: Wandering in Four Dimensions Part 12: Riemann's Solution Part 13: Riemann Surfaces Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.
Views: 2351196 Welch Labs
A Look at Some Higher Level Math Classes | Getting a Math Minor
 
15:55
MajorPrep Merch Store: https://teespring.com/stores/majorprep Join Facebook Group: https://www.facebook.com/groups/majorprep/ Follow MajorPrep on Twitter: https://twitter.com/MajorPrep1 This video goes over some of the extra math classes you can take if you get a math minor. Some of these include... Graph Theory Vector Analysis Topology Numerical Analysis Real Analysis Complex Analysis Abstract Algebra Differential Geometry etc If you want the full list of classes I show in this video you can click the link below. Full List of Required Math Classes: http://catalog.calpoly.edu/collegesandprograms/collegeofsciencemathematics/mathematics/mathematicsminor/ Cutting a Mobius Strip in Half (more detailed explanation): https://www.youtube.com/watch?v=XlQOipIVFPk ►Support the Channel Patreon: https://patreon.com/majorprep PayPal(one time donation): https://www.paypal.me/majorprep ►Check out the MajorPrep Amazon Store: https://www.amazon.com/shop/majorprep *************************************************** ► For more information on math, science, and engineering majors, check us out at https://majorprep.com Best Ways to Contact Me: Facebook, twitter, or email ([email protected])
Views: 137413 MajorPrep
Music And Measure Theory
 
13:13
A connection between a classical puzzle about rational numbers and what makes music harmonious.
Views: 467593 3Blue1Brown
Set Theory- An Introduction to Sets and Notation
 
05:48
I hope you found this video useful, please subscribe for daily videos! WBM Foundations: Mathematical logic Set theory Algebra: Number theory Group theory Lie groups Commutative rings Associative ring theory Nonassociative ring theory Field theory General algebraic systems Algebraic geometry Linear algebra Category theory K-theory Combinatorics and Discrete Mathematics Ordered sets Geometry Geometry Convex and discrete geometry Differential geometry General topology Algebraic topology Manifolds Analysis Calculus and Real Analysis: Real functions Measure theory and integration Special functions Finite differences and functional equations Sequences and series Complex analysis Complex variables Potential theory Multiple complex variables Differential and integral equations Ordinary differential equations Partial differential equations Dynamical systems Integral equations Calculus of variations and optimization Global analysis, analysis on manifolds Functional analysis Functional analysis Fourier analysis Abstract harmonic analysis Integral transforms Operator theory Numerical analysis and optimization Numerical analysis Approximations and expansions Operations research Probability and statistics Probability theory Statistics Computer Science Computer science Information and communication Applied mathematics Mechanics of particles and systems Mechanics of solids Fluid mechanics Optics, electromagnetic theory Classical thermodynamics, heat transfer Quantum Theory Statistical mechanics, structure of matter Relativity and gravitational theory Astronomy and astrophysics Geophysics applications Systems theory Other sciences Category
Views: 897 WelshBeastMaths
Manjul Bhargava - Lecture Series, Techfest 2015, IIT Bombay
 
45:44
Techfest, IIT Bombay presents one of the greatest minds of our time Professor Manjul Bhargava, an awardee of the Fields Medal also known as the 'Mathematics Nobel'. Professor Bhargava interacts with an audience of young students at Techest, IIT Bombay about 'square values of mathematical expressions, from ancient times to modern day'. About Professor Manjul Bhargava - Manjul Bhargava is an Indian-American mathematician. He is the R. Brandon Fradd Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorship at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to the number theory. Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves. He has an Erdos number of 2. Notable awards - Padma Bhushan (2015) Fields Medal (2014) Infosys Prize (2012) Fermat Prize (2011) Cole Prize (2008) Clay Research Award (2005) SASTRA Ramanujan Prize (2005) Blumenthal Award (2005) Hasse Prize (2003) Morgan Prize (1996) Hoopes Prize (1996) Lecture series at Techfest, IIT Bombay has hosted a large number of distinguished personalities from all across the globe like Pranav Mistry, Amartya Sen, Michael Sandel, Rakesh Sharma, Ei-chi-Nageshi, Gordon Day and Kiran Bedi helping to materialize the dreams of thousands of blooming young minds by providing a platform to connect and have an interaction of a lifetime. Techfest, Asia's Largest College Festival Visit us - www.techfest.org Like us at - https://www.facebook.com/iitbombaytechfest/ Subscribe us at - https://www.youtube.com/channel/UCech6f3osmQ_s54OsIZQDgA Follow us on Twitter : https://twitter.com/techfest_iitb?lang=en Follow us on Instagram: https://www.instagram.com/techfest_iitbombay/
Views: 40969 Techfest IIT Bombay
Jean Bourgain - Decoupling in harmonic analysis and applications to PDE and number theory
 
57:08
Princeton University - January 26, 2016 This talk was part of "Analysis, PDE's, and Geometry: A conference in honor of Sergiu Klainerman."
Views: 1021 princetonmathematics
Decoupling in harmonic analysis and applications to number theory - Jean Bourgain
 
55:07
Jean Bourgain IBM von Neumann Professor, School of Mathematics March 23, 2015 Decoupling inequalities in harmonic analysis permit to bound the Fourier transform of measures carried by hyper surfaces by certain square functions defined using the geometry of the hyper surface. The original motivation has to do with issues in PDE, such as smoothing for the wave equation and Strichartz inequalities for the Schrodinger equation on tori. It turns out however that these decoupling inequalities have surprizing number theoretical consequences,on which we will mainly focus. They include new bounds for the number of integral solutions to certain diagonal systems of polynomial equations and mean value theorems relevant to bounding exponential sums and the zeta function! In particular we make some further progress towards the Lindelof hypothesis using the Bombieri-Iwaniec method. More videos on http://video.ias.edu
Abelian Aariety ☆ Algebraic Theory ☆ Mathematics Lecture
 
01:17:17
lll➤ Gratis Crypto-Coins: https://crypto-airdrops.de ) More about Abelian varieties in thi algebraic theory video lecture. This is what you will learn in this lesson. Also have a look at the other parts of the course, and thanks for watching. In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. http://en.wikipedia.org/wiki/Abelian_variety This video was made ​​by another YouTube user and made available for the use under the Creative Commons licence "CC-BY". His channel can be found here: https://www.youtube.com/channel/UC5f0ii9uewnsgu0WuyNkfLQ
Basic complex analysis | Imaginary and complex numbers | Precalculus | Khan Academy
 
13:04
Argand Diagram, magnitude, modulus, argument, exponential form Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_analysis/v/absolute-value-of-a-complex-number?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus Missed the previous lesson? https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/multiplying-dividing-complex/v/dividing-complex-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Precalculus channel: https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 309716 Khan Academy
Geomagnetism ~ Carl Friedrich Gauss
 
14:57
Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy, Matrix theory, and optics. Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior to where it meets the solar wind, a stream of charged particles emanating from the Sun. Its magnitude at the Earth's surface ranges from 25 to 65 microtesla (0.25 to 0.65 gauss). Roughly speaking it is the field of a magnetic dipole currently tilted at an angle of about 10 degrees with respect to Earth's rotational axis, as if there were a bar magnet placed at that angle at the center of the Earth. Unlike a bar magnet, however, Earth's magnetic field changes over time because it is generated by a geodynamo (in Earth's case, the motion of molten iron alloys in its outer core).
Views: 7181 Dap Dapple
5.6 P. Sarnak : Some problems in number theory and analysis
 
53:55
Visions in Mathematics Towards 2000 All videos playlist https://www.youtube.com/playlist?list=PLP0YToNcfAwLBd8yibTtjv3aHfcbT4GBA The Proceeding of this conference was published by Birkhauser in two parts, and also represent the Volume 2000 of GAFA: https://books.google.ru/books?id=kQtYL7pUWSwC&printsec=frontcover&hl=ru#v=onepage&q&f=false https://books.google.ru/books?id=MNpJ4voD5PQC&printsec=frontcover&hl=ru#v=onepage&q&f=false Wednesday, August 25, 1999, 9:15-15:00 1.0 Introduction by U.Liberman and V.Milman 1.1 M. Gromov : Geometry as the art of asking questions 1.2 H. Hofer : Holomorphic curves and real three-dimentional dynamics 1.3 Y. Eliashberg : Symplectic field theory 1.4 H. Furstenberg : Dynamical methods in Diophantine problems Wednesday, August 25, 1999, 15:00-18:00 1.5 G. Margulis : Diophantine approximation, lattices and flows on homogeneous spaces 1.6 Y. Sinai : On some problems in the theory of dynamical systems and mathematical physics 1.7 Discussion of the subjects of lectures, Day August 25 with introduction by Y. Sinai (Zakharov, Shnirelman, Hofer) Thursday, August 26, 1999, 9:00-12:00 2.1 J. Fröhlich: Large quantum systems 2.2 Y. Ne'eman : Physics as geometry – Plato vindicated 2.3 A. Connes : Non-commutative geometry Thursday, August 26, 1999, 13:00-18:00 2.4 P. Shor : Mathematical problems in quantum information theory 2.5 A. Razborov : Complexity of proofs and computation 2.6 A. Wigderson : Some fundamental insights of computational complexity 2.7 M. Rabin : The mathematics of trust and adversity Friday, August 27, 1999, 14:00-18:00, Moriah Hotel, Dead Sea 3.1 A. Jaffe : Mathematics of quantum fields 3.2 S. Novikov : Topological phenomena in real physics 3.3 Discussion on Mathematical Physics with introduction by A. Connes 3.4 Discussion on Geometry with introduction by M. Gromov Sunday, August 29, 1999, 10:00-12:00, 14:00-16:00, Moriah Hotel, Dead Sea 4.1 Discussion on Mathematics in the Real World (image, applications etc.) with introduction by R. Coifman 4.2 Discussion on Computer Science and Discrete Mathematics with introduction by M. Rabin Monday, August 30, 1999, 9:00-12:30 5.1 R. Coifman : Challenges in analysis 1 5.2 P. Jones : Challenges in analysis 2 5.3 E. Stein : Some geometrical concepts arising in harmonic analysis 5.4 Discussion of the subjects of lectures, Morning August 30 Monday, August 30, 1999, 14:30-18:00 5.5 H. Iwaniec : Automorphic forms in recent developments of analytic number theory 5.6 P. Sarnak : Some problems in number theory and analysis 5.7 D. Zagier : On "q" (or "Connections between modular forms, combinatorics and topology") 5.8 Discussion "The unreasonable effectiveness of modular forms" introduced by P. Sarnak Tuesday, August 31, 1999, 9:00-13:00 6.1 L. Lovász : Discrete and continuous: two sides of phenomena 6.2 N. Alon : Probabilistic and algebraic methods in discrete mathematics 6.3 G. Kalai : An invitation to Tverberg's theorem 6.4 Discussion of the subjects of lectures, Morning August 31 Tuesday, August 31, 1999, 14:30-19:00 6.5 T. Gowers : Rough structure and crude classification 6.6 J. Bourgain : Some problems in Hamiltonian PDE's 6.7 V. Milman : Topics in geometric analysis 6.8 Discussion of the subjects of lectures, Evening August 31 Wednesday, September 1, 1999, 9:00-12:30 7.1 S. Bloch : Characteristic classes for linear differential equations 7.2 V. Voevodsky : Motivic homotopy types 7.3 D. Kazhdan : The lifting problems and crystal base Wednesday, September 1, 1999, 14:30-18:40 7.4 A. Beilinson : Around geometric Langlands 7.5 J. Bernstein : Equivariant derived categories 7.6 V. Kac : Classification of infinite-dimensional simple groups of supersymetries and quantum field theory 7.7 Discussion of the subjects of lectures, Evening September 1 Thursday, September 2, 1999, 9:00-12:50 8.1 R. MacPherson : On the applications of topology 8.2 M. Kontsevich : Smooth and compact 8.3 D. Sullivan : String interactions in topology 8.4 Discussion of the subjects of lectures, Morning September 2 Thursday, September 2, 1999, 14:30-19:00 8.5 R.J. Aumann : Mathematical game theory: Looking backward and forward 8.6 E. Hrushovski : Logic and geometry 8.7 Discussion of the subjects of lectures, Evening September 2 8.8 Discussion "The role of homotopical algebra in physics" with introductions by D. Sullivan and M. Kontsevich Friday, September 3, 1999, 9:00-13:30 9.1 T. Spencer : Universality and statistical mechanics 9.2 E. Lieb : The mathematics of the second law of thermodynamics 9.3 A. Kupiainen : Lessons for turbulence 9.4 S. Klainerman : Some general remarks concerning nonlinear PDE's 9.5 Discussion of the subjects of lectures, Day September 3
Part I: Complex Variables, Lec 1: The Complex Numbers
 
43:37
Part I: Complex Variables, Lecture 1: The Complex Numbers Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 289780 MIT OpenCourseWare
Geometry with complex numbers | Argument of complex numbers
 
19:20
Buy JEE Maths video lectures : Call 07814166606, 0172-4280095, Visit our website http://www.tewanimaths.com Prof. Ghanshyam Tewani is author of many books on IITJEE mathematics published by worlds one of the most renowned publisher CENGAGE LEARNING. These books are appreciated all over INDIA and abroad. These books are now one of the top selling books in INDIA. Some books authored by Prof. Ghanshyam Tewani are 1. Algebra 2. Coordinate Geometry 3. Trigonometry 4. Calculus 5. Vectors and 3-D Geometry Prof. Ghanshyam Tewani has experience of 15 years for training students in Mathematics for IITJEE and other competitive examinations. He has worked for four years for FIITJEE Ltd., Delhi , the renowned name in IITJEE coaching. He is a rare genius, acknowledged as one of the best national level teachers in mathematics. His intense and concise lectures are aimed at clearing the student's fundamental concepts in mathematics and at the same time, laying a strong foundation for better understanding of complex problems. A man of uncommon devotion, he leaves no stone unturned to help out needy and deserving students. Every single word he speaks is weighed, for he believes in precision. In his own words, "For me each student counts, each one must learn to the best of his / her capability." Being a perfectionist, he doesn't tolerate even a minor error. It is not surprising that the best & most brilliant of student community hold him as their ideal and an adored mentor. Our Mission To develop a strong base with deeper understanding, and strengthen theoretical and applied dimensions of mathematics. To equip the students with a set of conceptual skills, intuitive tricks and fast methods to make them more confident and consequently expel the baseless fear of mathematics. (Buy iitjee videos : Call 07814166606, 0172-4280095, Visit our website www.tewanimaths.com)
College Algebra: Factoring by Grouping
 
02:25
http://www.mindbites.com/lesson/3014 Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found athttp://www.thinkwell.com/student/product/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Views: 1991 Mindbitesdotcom
2017 Breakthrough Prize in Mathematics awarded to Jean Bourgain
 
02:08
December 5, 2016 - NAS foreign associate Jean Bourgain was awarded the 2017 Breakthrough Prize in Mathematics. Jean Bourgain is IBM von Neumann Professor in the School of Mathematics at the Institute for Advanced Study, Princeton, New Jersey. He was awarded the Prize for multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory. This video was created by National Geographic and The Breakthrough Prize. You can learn more about his work at http://www.nasonline.org/member-directory/members/20024877.html
Math Antics - Mean, Median and Mode
 
11:04
Learn More at mathantics.com Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
Views: 775181 mathantics
Quick; What is the p-value?
 
03:01
I hope you found this video useful, please subscribe for daily videos! WBM Foundations: Mathematical logic Set theory Algebra: Number theory Group theory Lie groups Commutative rings Associative ring theory Nonassociative ring theory Field theory General algebraic systems Algebraic geometry Linear algebra Category theory K-theory Combinatorics and Discrete Mathematics Ordered sets Geometry Geometry Convex and discrete geometry Differential geometry General topology Algebraic topology Manifolds Analysis Calculus and Real Analysis: Real functions Measure theory and integration Special functions Finite differences and functional equations Sequences and series Complex analysis Complex variables Potential theory Multiple complex variables Differential and integral equations Ordinary differential equations Partial differential equations Dynamical systems Integral equations Calculus of variations and optimization Global analysis, analysis on manifolds Functional analysis Functional analysis Fourier analysis Abstract harmonic analysis Integral transforms Operator theory Numerical analysis and optimization Numerical analysis Approximations and expansions Operations research Probability and statistics Probability theory Statistics Computer Science Computer science Information and communication Applied mathematics Mechanics of particles and systems Mechanics of solids Fluid mechanics Optics, electromagnetic theory Classical thermodynamics, heat transfer Quantum Theory Statistical mechanics, structure of matter Relativity and gravitational theory Astronomy and astrophysics Geophysics applications Systems theory Other sciences Category
Views: 131 WelshBeastMaths
Integrate Using U-Substitution #3
 
04:20
I hope you found this video useful, please subscribe for daily videos! WBM Foundations: Mathematical logic Set theory Algebra: Number theory Group theory Lie groups Commutative rings Associative ring theory Nonassociative ring theory Field theory General algebraic systems Algebraic geometry Linear algebra Category theory K-theory Combinatorics and Discrete Mathematics Ordered sets Geometry Geometry Convex and discrete geometry Differential geometry General topology Algebraic topology Manifolds Analysis Calculus and Real Analysis: Real functions Measure theory and integration Special functions Finite differences and functional equations Sequences and series Complex analysis Complex variables Potential theory Multiple complex variables Differential and integral equations Ordinary differential equations Partial differential equations Dynamical systems Integral equations Calculus of variations and optimization Global analysis, analysis on manifolds Functional analysis Functional analysis Fourier analysis Abstract harmonic analysis Integral transforms Operator theory Numerical analysis and optimization Numerical analysis Approximations and expansions Operations research Probability and statistics Probability theory Statistics Computer Science Computer science Information and communication Applied mathematics Mechanics of particles and systems Mechanics of solids Fluid mechanics Optics, electromagnetic theory Classical thermodynamics, heat transfer Quantum Theory Statistical mechanics, structure of matter Relativity and gravitational theory Astronomy and astrophysics Geophysics applications Systems theory Other sciences Category
Views: 60 WelshBeastMaths
Math 101 Introduction to Analysis 091115: Basics (Rational Zeroes Theorem)
 
45:14
Definition of algebraic numbers; the root of 2 is algebraic (and not rational); Rational Zeroes theorem; alternate proof that the root of 2 is irrational.
Views: 1110 Winston Ou
Visualizing the Riemann hypothesis and analytic continuation
 
22:11
Understanding the Riemann hypothesis requires understanding a certain function which is famously confusing outside its "domain of convergence", but a certain visualization sheds light on how it extends. There are posters for this visualization of the zeta function at http://3b1b.co/store Thank you to everyone supporting on Patreon: https://www.patreon.com/3blue1brown Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Check out some of Vince's other work here: http://www.vincentrubinetti.com/ For those who want to learn more about complex exponentiation, here are a few resources: - My video on the topic: http://youtu.be/mvmuCPvRoWQ - Mathologer's: https://youtu.be/-dhHrg-KbJ0 - Better Explained: https://goo.gl/z28x2R For those who want to learn more about the relationship between 1+2+3+4+... and -1/12, I'm quite fond of this blog post by Terry Tao: https://goo.gl/XRzyTJ Also, in a different video "What does it feel like to invent math", I give a completely different example of how adding up growing positive numbers can meaningfully give a negative number, so long as you loosen your understanding of what distance should mean for numbers: https://youtu.be/XFDM1ip5HdU Interestingly, that vertical line where the convergent portion of the function appears to abruptly stop corresponds to numbers whose real part is Euler's constant, ~0.577. For those who know what this is, it's kind of fun to puzzle about why this is the case. Special shout-outs to the following Patreon supporters: CrypticSwarm, Ali Yahya, Dave Nicponski, Damion Kistler, Juan Batiz-Benet, Yu Jun, Othman Alikhan, Markus Persson, Joseph John Cox, Luc Ritchie, Shimin Kuang, Einar Wikheim Johansen, Rish Kundalia, Achille Brighton, Kirk Werklund, Ripta Pasay, Felipe Diniz, dim85, Chris , Michael Rabadi, Alexander Juda, Mads Elvheim, Joseph Cutler, Curtis Mitchell, Ari Royce, Bright , Myles Buckley, Andy Petsch, Otavio Good, Karthik T, Steve Muench, Viesulas Sliupas, Steffen Persch, Brendan Shah, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, aidan boneham, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Jeffrey Herman, Jacob Young and Steve Muench. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1392190 3Blue1Brown
Introduction to Math Analysis (Lecture 1): The Need for Real Numbers
 
01:19:40
This is the first lecture in a course titled "Intro to Math Analysis". This is a test video, but with any luck, the full sequence of lectures will be published at some point.
Views: 36153 Arkady Etkin
Lecture Series: "p-adic Geometry" by Peter Scholze [2014] (lecture 1)
 
01:14:43
Full-course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpixcWT-mYCs2G-0rUWs9wtYX Fall 2014 MATH 274 Topics in Algebra: "p-adic Geometry" by Peter Scholze http://www.msri.org/web/msri/online-videos/scholze-lecture-fall-2014 https://math.berkeley.edu/courses/fall-2014-math-274-001-lec
Views: 1963 Graduate Mathematics
algebra part 1 in english
 
11:54
algebra is a branch of maths together with number theory,geometry and analysis.In part 1 we will discuss about variable,literal,co efficient,terms,algebraic expressions,arithmetic operations on terms and expressions,the ways to do arithmetic operations,etc.these are explained clearly in english by dk if you like the video like it if you dislike the video please dislike it.Comment the video below.But don't forget to subscribe. enjoy watching and keep smiling by dk if you want to download or watch live at https://youtu.be/nGAHZ2ABoWY
Views: 20 dk knowhub
College Algebra: Factoring: Greatest Common Factor
 
02:23
http://www.mindbites.com/lesson/3013 Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found athttp://www.thinkwell.com/student/product/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Views: 1299 Mindbitesdotcom
Decoupling in harmonic analysis and applications to number theory - Jean Bourgain
 
01:20:33
Jean Bourgain IBM von Neumann Professor, School of Mathematics March 23, 2015 Decoupling inequalities in harmonic analysis permit to bound the Fourier . Princeton University - January 26, 2016 This talk was part of Analysis, PDEs, and Geometry: A conference in honor of Sergiu Klainerman. Topic: Decoupling in harmonic analysis and the Vinogradov mean value theorem Speaker: Jean Bourgain Date: Thursday, December 17 Based on a new . We explain how a certain decoupling theorem from Fourier analysis finds sharp applications in PDEs, incidence geometry and analytic number theory. This is .
Views: 20 Olivia Frank
College Algebra - Lecture 5 - More numbers and Geometry
 
40:43
College Algebra with Professor Richard Delaware - UMKC VSI - Lecture 5 - More numbers and Geometry. In this Lecture,we learn about Complex numbers,some area formulae and the Pythagorean theorem.
Views: 60287 UMKC

Drafting cover letter samples
Polizeiwissenschaft newsletter formats
Chcbp application letters
Resume cover letter example australian
Article writing service