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- 13:51, 6 December 2020 Introduction to Hidden Markov Chains (hist) [3,438 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Hidden Markov Chains= The idea of the hidden Markov chain was raised by an American mathematician Leonard Baum and his colleagues...")
- 12:23, 6 December 2020 Walther MA271 Fall2020 topic1: Fields (hist) [1,914 bytes] Merrill8 (Talk | contribs)
- 04:07, 6 December 2020 Sphere Packing 8: Works Cited (hist) [1,404 bytes] Elechien (Talk | contribs) (Created page with "<center> ===Works Cited=== ''Author: Eli LeChien'' </center> Darling, D. (n.d.). Cannonball problem. Retrieved December 06, 2020, from <p> https://www.daviddarling.info/en...")
- 04:01, 6 December 2020 Sphere Packing 7: Conclusion (hist) [977 bytes] Elechien (Talk | contribs) (Created page with "<center> ===Conclusion=== ''Author: Eli Lechien'' <center> In mathematics, sometimes a problem that appears difficult can be solved in an incredibly simple manner when look...")
- 03:51, 6 December 2020 Sphere Packing 6: Applications of Higher Dimensional Packings (hist) [2,703 bytes] Elechien (Talk | contribs) (Created page with "<center> ===Applications of Higher Dimensional Sphere Packings=== ''Author: Eli LeChien'' <h1 style = "font-size:110%"> Error-Correcting Code </h1> </center> Sphere packin...")
- 03:31, 6 December 2020 Restrictions of Stationary Distribution (hist) [1,598 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Restrictions of Stationary Distribution In the last section, it is emphasized that steady-state vectors can be derived only with...")
- 03:11, 6 December 2020 Sphere Packing 5: Density of Silver (hist) [2,280 bytes] Elechien (Talk | contribs) (Created page with "<center> === Density of Silver === ''Author: Eli LeChien''</center> But what are the ramifications of this century-long proof? Does it have the same universe-unlocking abil...")
- 02:50, 6 December 2020 Markov Chain References and Additional Readings (hist) [2,130 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Additional Readings= https://www.math.fsu.edu/~cstover/teaching/sp18_mas3105/handouts/ch1/REFetc.pdf - An introduction to element...")
- 02:37, 6 December 2020 Sphere Packing 4: Kepler's Conjecture Intuition (hist) [3,440 bytes] Elechien (Talk | contribs) (Created page with "<center>===Kepler's Conjecture Intuition=== ''Author: Eli LeChien''</center> The same method applied in the last section could be extended to the three dimensional case wit...")
- 02:35, 6 December 2020 Sources (hist) [1,806 bytes] Hmalladi (Talk | contribs) (Created page with "'''SOURCES''' #Bovykin, A. (2007). Brief introduction to unprovability [Scholarly project]. In Cs.umd.edu. Retrieved December 05, 2020, from https://www.cs.umd.edu/~gasarch/T...")
- 02:25, 6 December 2020 Conclusion (hist) [1,220 bytes] Hmalladi (Talk | contribs) (Created page with "'''CONCLUSION''' The world of mathematics fell apart when Gödel’s Theorems came to the forefront of the field. For most of the history of mathematics, it was assumed that...")
- 02:22, 6 December 2020 Discussion about Gödel’s Theorems (hist) [5,703 bytes] Hmalladi (Talk | contribs) (Created page with "'''DISCUSSION''' Many mathematicians upon the unveiling of Gödel’s Incompleteness Theorem held the belief that while Gödel’s logic and proof was sound, the systems he w...")
- 02:14, 6 December 2020 123456789 (hist) [0 bytes] Elechien (Talk | contribs)
- 02:14, 6 December 2020 Gödel’s Second Theorem (hist) [4,556 bytes] Hmalladi (Talk | contribs) (Created page with "'''GÖDEL’S SECOND THEOREM''' Gödel’s Second Incompleteness Theorem is most simply stated as follows: <center>“It is impossible for any sufficiently expressive and c...")
- 01:59, 6 December 2020 Gödel’s First Theorem (hist) [9,936 bytes] Hmalladi (Talk | contribs) (Created page with "'''GÖDEL’S FIRST THEOREM''' Gödel’s first incompleteness theorem is most simply stated as follows: “There exists no sufficiently expressive system that is consistent...")
- 01:56, 6 December 2020 Markov Chain Theorems (hist) [3,172 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Markov Chain Theorems= A transition matrix is considered '''regular''' if it has all positive entries. This is reflected in our e...")
- 01:43, 6 December 2020 An Introduction to Gödel’s Incompleteness Theorems (hist) [1,211 bytes] Hmalladi (Talk | contribs) (Created page with "'''INTRODUCTION''' In 1931 Kurt Gödel published his Incompleteness Theorem, now known as Gödel’s Incompleteness Theorem. Gödel, an Austrian logician, had managed to prov...")
- 01:38, 6 December 2020 Recurrent State and Transient State (hist) [975 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Recurrent State and Transient State= The recurrence probability examines whether the Markov chain can return to a state again n-s...")
- 01:29, 6 December 2020 Periodicity of Markov Chains (hist) [1,351 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Periodicity of Markov Chains= Let us denote <math>d_{i}</math> as the greatest common divisor of the number set <math>{n:n\geq1,...")
- 01:13, 6 December 2020 Communication and Reducibility (hist) [2,419 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Communication and Reducibility= Before moving on and discovering more behaviors of Markov chains, we need to classify the propert...")
- 01:06, 6 December 2020 Sphere Packing 3: Packing Basics (hist) [4,073 bytes] Elechien (Talk | contribs) (Created page with "=== Packing Basics: A Warm Up=== ''Author: Eli LeChien'' To gain understanding Kepler's solution, it is first useful to define exactly what is meant by a “packing density...")
- 00:54, 6 December 2020 MA271Fall2020Walther Topic27 Quasicrystals (hist) [4,327 bytes] Gthiruna (Talk | contribs) (Created page with "=Quasicrystals= Penrose Tiling Home Previous Section: Robinson Triangles ___________...")
- 00:50, 6 December 2020 Sphere Packing 0: Table of Contents (hist) [636 bytes] Elechien (Talk | contribs)
- 00:49, 6 December 2020 Sphere Packing 2: A Brief History (hist) [1,691 bytes] Elechien (Talk | contribs) (Created page with "=== A Brief History of the Sphere Packing Problem === ''Author: Eli LeChien'' Sir Walter Raleigh was a famous British explorer, although some consider him to be more akin to...")
- 00:48, 6 December 2020 MA271Fall2020Walther Topic27 Robinson Triangles (hist) [2,102 bytes] Gthiruna (Talk | contribs) (Created page with "=Robinson Triangles= Penrose Tiling Home Previous Section: Golden Ratio MA271Fall2020Wal...")
- 00:47, 6 December 2020 Sphere Packing Home: Table of Contents (hist) [0 bytes] Elechien (Talk | contribs)
- 00:45, 6 December 2020 MA271Fall2020Walther Topic27 Golden Ratio (hist) [4,980 bytes] Gthiruna (Talk | contribs) (Created page with "Penrose Tiling Home MA271Fall2020Walther_Topic27_Third Penrose Tiling/Rhombus Tiling (P3)|Previous Section: Third Penrose Tiling/Rhombus...")
- 00:45, 6 December 2020 Python Demonstration (hist) [4,504 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Python Demonstration= We will be using Python to demonstrate Markov chains. The following program was taken from [https://towards...")
- 00:38, 6 December 2020 N-th Term Transition (hist) [2,452 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =n-th Term Transition= Because of the limited dependence property of the Markov chain, we can use the transition matrix <math>P</m...")
- 00:29, 6 December 2020 Sphere Packing 1: Introduction (hist) [1,294 bytes] Elechien (Talk | contribs) (Created page with "=== Introduction to Sphere Packing === ''Author: Eli LeChien'' Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined math...")
- 00:18, 6 December 2020 Sphere Packing: Table of Contents (hist) [0 bytes] Elechien (Talk | contribs)
- 00:15, 6 December 2020 Sphere Packing: Introduction (hist) [0 bytes] Elechien (Talk | contribs) (Created page with "=== An Introduction to Sphere Packing=== ''Author: Eli LeChien'' Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined ma...")
- 00:14, 6 December 2020 Laplace Operator Page 1 2020 (hist) [1,885 bytes] Denneyl (Talk | contribs) (Created page with "Category:MA271Fall2020Walther Back to main page")
- 00:10, 6 December 2020 Laplace Operator Page 2 2020 (hist) [3,797 bytes] Denneyl (Talk | contribs) (Created page with "The Laplace operator, represented by <math>\Delta</math>, is defined as the divergence of the gradient of a function. <math> {\large\Delta = \nabla\cdot\nabla = \nabla^{2} =...")
- 00:10, 6 December 2020 WaltherMA271Fall2020: Sphere Packing: A Brief History (hist) [0 bytes] Elechien (Talk | contribs) (Created page with "=== A Brief History of the Sphere Packing Problem=== ''Author: Eli LeChien Sir Walter Raleigh was a famous British explorer, although some consider him to be more akin to a...")
- 00:09, 6 December 2020 Walther MA271 Fall2020 topic1: A Note on Groups (hist) [3,341 bytes] Merrill8 (Talk | contribs)
- 00:06, 6 December 2020 Walther MA271 Fall2020 topic3 (hist) [12,746 bytes] Chakra55 (Talk | contribs) (Created page with " == The Fundamental Group == == By == == Aneesh Chakravarthula == == Table of contents == * Introduction * Definitions * The Fundamental Group * Unit Circle * 2-Spher...")
- 00:05, 6 December 2020 Sphere Packing: A Brief History (hist) [973 bytes] Elechien (Talk | contribs) (Created page with "Sir Walter Raleigh was a famous British explorer, although some consider him to be more akin to a pirate. He asked one of his assistants, mathematician and astronomer Thomas H...")
- 23:58, 5 December 2020 WaltherMA271Fall2020: Sphere Packing: Introduction (hist) [0 bytes] Elechien (Talk | contribs) (Created page with "=== An Introduction to the Sphere Packing Problem === Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined mathematically a...")
- 23:53, 5 December 2020 Walther MA271 Fall2020 topic1: References and Further Reading (hist) [2,271 bytes] Merrill8 (Talk | contribs)
- 23:52, 5 December 2020 Further Reading and References (hist) [2,287 bytes] Jmworthi (Talk | contribs)
- 23:51, 5 December 2020 A Brief History (hist) [995 bytes] Elechien (Talk | contribs) (Created page with "Sir Walter Raleigh was a famous British explorer, although some consider him to be more akin to a pirate. He asked one of his assistants, mathematician and astronomer Thomas H...")
- 23:51, 5 December 2020 Applications (hist) [3,911 bytes] Jmworthi (Talk | contribs)
- 23:51, 5 December 2020 Worked Examples Using Nyquist’s Theorem (hist) [3,619 bytes] Jmworthi (Talk | contribs)
- 23:50, 5 December 2020 Features of Nyquist's Theorem (hist) [2,752 bytes] Jmworthi (Talk | contribs)
- 23:50, 5 December 2020 Transition Probability Matrix (hist) [2,233 bytes] Nlfang (Talk | contribs) (Created page with "Category:Walther MA271 Fall2020 topic2 =Transition Probability Matrix= However, using a tree diagram also has its limitations: if we want to calculate the probability af...")
- 23:49, 5 December 2020 Definition of Nyquist’s Theorem (hist) [4,421 bytes] Jmworthi (Talk | contribs)
- 23:44, 5 December 2020 WaltherMA271Fall2020: Sphere Packing History (hist) [1,054 bytes] Elechien (Talk | contribs) (Created page with "=== A Brief History of the Sphere Packing Problem === Sir Walter Raleigh was a famous British explorer, although some consider him to be more akin to a pirate. He asked one o...")
- 23:12, 5 December 2020 WaltherMA271Fall2020: Introduction (hist) [1,173 bytes] Elechien (Talk | contribs) (Created page with "Spheres are one of the most fundamental shapes that make up the universe. A sphere can easily be defined mathematically as the three dimensional set of points equidistant from...")
- 23:08, 5 December 2020 Walther MA271 Fall2020 topic7 Bibliography (hist) [1,591 bytes] Babelman (Talk | contribs)
