Math 101 Introduction to Analysis 09 092017 The Extended Real Number System; Sequences
Extended real number system as a set; as an ordered set. Comment: all nonempty subsets have least upper bounds. Is not a field. Conventions. Definition of a sequence. Examples of sequences.
From playlist Course 6: Introduction to Analysis (Fall 2017)
The extended rational numbers in practice | Real numbers and limits Math Foundations 105
We review the extended rational numbers, which extend the rational numbers to all expressions of the form a/b, where a and b are integers---even b=0. Then we give some examples of how these strange beasts might prove useful in mathematics. But first we give one example of where they are un
From playlist Math Foundations
What are Real Numbers? | Don't Memorise
Watch this video to understand what Real Numbers are! To access all videos on Real Numbers, please enroll in our full course here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=3YwrcJxEbZw&utm_term=%7Bkeyword%7D In this video, w
From playlist Real Numbers
Intermediate Algebra-Complex Numbers
Intermediate Algebra-Complex Numbers
From playlist Intermediate Algebra
Geometry of Complex Numbers (2 of 6: Real vs. Complex)
More resources available at www.misterwootube.com
From playlist Introduction to Complex Numbers
Set Theory (Part 14a): Constructing the Complex Numbers
Please leave your thoughts and questions below! In this video, we will extend the real numbers to the complex numbers and investigate the algebraic structure of the complex numbers after defining addition and multiplication of these new objects. We will also begin to see how complex numbe
From playlist Set Theory by Mathoma
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
Visualizing the Riemann zeta function and analytic continuation
Unraveling the enigmatic function behind the Riemann hypothesis Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/zeta-thanks Home page: https://www.3b
From playlist Explainers
Analytic Continuation and the Zeta Function
Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co
From playlist Analytic Number Theory
Riemann Hypothesis - Numberphile
Featuring Professor Edward Frenkel. 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 boo
From playlist Edward Frenkel on Numberphile
Tropical Geometry - Lecture 11 - Toric Varieties | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
Pascal's wager and real numbers
My entry for 3blue1brown's contest, talking about Pascal's wager and how it leads to interesting questions about (hyper)real numbers. A big shoutout to Grant for coming up with this wonderful idea. Link to Thierry Platinis channel for more on hyperreal numbers: https://www.youtube.com/cha
From playlist Summer of Math Exposition Youtube Videos
Set Theory (Part 14): Real Numbers as Dedekind Cuts
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will construct the real number system as special subsets of rational numbers called Dedekind cuts. The trichotomy law and least upper bound property of the reals will also be proven. T
From playlist Set Theory by Mathoma
When do fractional differential equations have solutions that extend?
When do fractional differential solutions have solutions that extend? New research to appear in Journal of Classical Analysis! http://files.ele-math.com/articles/jca-05-11.pdf doi:10.7153/jca-05-11 This note discusses the question: When do nonlinear fractional differential equations of a
From playlist Mathematical analysis and applications
Around the Davenport-Heilbronn Function - Enrico Bombieri
Enrico Bombieri Institute for Advanced Study November 10, 2011 The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann
From playlist Mathematics
Complex Analysis - Part 31 - Applications of the Identity Theorem
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From playlist Complex Analysis
G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)
In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem affords an interpretation in terms of both holomorphic and non-holomorphic modular forms. The
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Math 101 Introduction to Analysis 092315: Introduction to the limit
The extended real number system (an ordered set, but not a field; all sets have least upper bounds). Introduction to the rigorous definition of limit (for sequences).
From playlist Course 6: Introduction to Analysis