, 2021. An exciting breakthrough by an academic little known before last year is firing up mathematicians. When his paper got accepted, Zhang said he expected the formulas contained therein to form the basis for narrowing the 70 million gap. Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He is a recipient of the 2014 MacArthur award,[27] and was elected as an Academia Sinica Fellow during the same year. 25. Yitang Zhang (Chinese: ; born February 5, 1955) is a Chinese American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015. He explains everything clearly for the lecture. After receiving his master's degree in mathematics, with recommendations from Professor Ding Shisun, the President of Peking University, and Professor Deng Donggao, Chair of the university's Math Department,[11] Zhang was granted a full scholarship at Purdue University. [14], After some years, Zhang managed to find a position as a lecturer at the University of New Hampshire, where he was hired by Kenneth Appel in 1999. 2023 CNET, a Red Ventures company. The American Journal of Human Genetics 109 (5), 802-811, Y Zhang, K Liang, M Liu, Y Li, H Ge, H Zhao, Machine Learning in Computational Biology 2019 Proceedings. The exams were super easy though. [16] Zhang stayed for a semester at The Institute For Advanced Study in Princeton, NJ in 2014, and he joined the University of California, Santa Barbara in fall 2015.[17]. 2015. Yitang Dai. The Journal of Physical Chemistry Letters 6 (20), 4159-4164. , 2015. Delivered Wednesdays. Y Zhang, Q Lu, Y Ye, K Huang, W Liu, Y Wu, X Zhong, B Li, Z Yu, Y Zhang, Y Cheng, W Jiang, Y Ye, Q Lu, H Zhao, Briefings in bioinformatics 22 (5), bbaa442. Saturday, April 7, 2018 Professor Yitang Zhang has been recognized with a Distinguished Lifetime Achievement Award from the Asian American Engineer of the Year (AAEOY) 2018 Award program. He also worked in a motel in Kentucky and in a Subway sandwich shop. A true gift to have learned from Dr. Zhang. Zhang arrived at Purdue in January 1985, studied there for six and a half years, and obtained his PhD in mathematics in December 1991. Fortunately, lectures are recorded and his notes are exceedingly clear. 25. The ones marked * may be different from the article in the profile. [11] In a detailed profile published in The New Yorker magazine in February 2015, Alec Wilkinson wrote Zhang "parted unhappily" with Moh, and that Zhang "left Purdue without Moh's support, and, having published no papers, was unable to find an academic job". In a 2013 interview with Nautilus magazine, Zhang said he did not get a job after graduation. [7] In 2018, responding to reports of his treatment of Zhang, Moh posted an update on his website. (1982) and M.S. Anyone salty about him literally had to have put 0 effort into his class. 110 (3) 555 - 572, 1 December 2001. https://doi.org/10.1215/S0012-7094-01-11034-X Information Published: 1 December 2001 First available in Project Euclid: 18 June 2004 zbMATH: 1012.11081 MathSciNet: MR1869116 Yitang Zhang is a mathematician who emerged from relative obscurity with a landmark achievement in analytic number theory: the so-called bounded prime gap, which essentially establishes that the difference in spacing between two consecutive prime numbers is, infinitely often, bounded by a fixed number. "And now we've got somebody who's literally come of nowhere, that no one expected to produce this kind of results, and has done something impressive that many great minds were unable to do.". At around the age of nine, he found a proof of the Pythagorean theorem. Midterms and Finals are extremely reasonable and fair considering how much prep material he releases. [4], Previously working at the University of New Hampshire as a lecturer, Zhang submitted a paper to the Annals of Mathematics in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. 133. Hope he succeeds again and becomes a legendary mathematician! However attending classes would give basic ideas about materials in homework and exams. Highly recommend. Yitang Zhang. Try again later. University of Nottingham physicist Ed Copeland uses a pen and paper to explain Yitang Zhang's finding on bounded gaps between prime numbers. Heavy accent and not very tech savvy. Don't take his online class, he is not a tech person. Zhang himself says that "something impressive" probably has no practical application, though prime numbers do extend beyond the realm of pure math into more real-world uses. Z Jiang, J He, SA Deshmukh, P Kanjanaboos, G Kamath, Y Wang, X He, H Fang, DJ Gosztola, Z Jiang, P Jena, WN Wang, ACS applied materials & interfaces 11 (13), 12516-12524, J He, A Towers, P Yuan, J Zhang, J Chen, AJ Gesquiere, ST Wu, Y Dong, T Sun, Z Jiang, J Strzalka, L Ocola, J Wang, Z Jiang, XM Lin, M Sprung, S Narayanan, J Wang, CM Evans, S Narayanan, Z Jiang, JM Torkelson, New articles related to this author's research, GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films, Nanostructured polymer films with metal-like thermal conductivity, Surpassing 10% Efficiency Benchmark for Nonfullerene Organic Solar Cells by Scalable Coating in Air from Single Nonhalogenated Solvent, Molecular engineered conjugated polymer with high thermal conductivity, The dedicated high-resolution grazing-incidence X-ray scattering beamline 8-ID-E at the Advanced Photon Source, Influence of Hydrophobicity on Polyelectrolyte Complexation, Monolayer Perovskite Bridges Enable Strong Quantum Dot Coupling for Efficient Solar Cells, Structure-induced Enhancement of Thermal Conductivities in Electrospun Polymer Nanofibers, Xray Photon Correlation Spectroscopy Studies of Surfaces and Thin Films, Evidence for viscoelastic effects in surface capillary waves of molten polymer films, Xi-cam: a versatile interface for data visualization and analysis, Nanoparticle assemblies in thin films of supramolecular nanocomposites, Structure of Polyelectrolyte Brushes in the Presence of Multivalent Counterions, Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films, Subnanometre ligand-shell asymmetry leads to Janus-like nanoparticle membranes, Mechanistic Insight into Photocatalytic Pathways of MIL-100 (Fe)/TiO2 Composites, In-situ Synthesis and Macroscale Alignment of CsPbBr3 Perovskite Nanorods in Polymer Matrix, Three-dimensional coherent X-ray surface scattering imaging near total external reflection, Capturing the crystalline phase of two-dimensional nanocrystal superlattices in action, Modulus, confinement, and temperature effects on surface capillary wave dynamics in bilayer polymer films near the glass transition. The ones marked, Journal of Applied Crystallography 48 (3), 917-926. 86 on the final, 78 on the midterm, 100 on the homework, but a 67% on the quizes due to them being at 8am and missing two. Our method is a re nement of the recent work of Goldston, Pintz and Y ld r m on the 4. One of the most brilliant minds of our time. Besides, he gave practice exams that are very similar to the actual exams, so be sure to understand how to solve them. In his paper, Zhang obtained for the first time an unconditional advance on : Theorem 6 (Zhang) is true for all . Also, he announces what the quiz will cover in the lecture. The Journal of Physical Chemistry Letters 2 (2), 48-54, CG Elles, CA Rivera, Y Zhang, PA Pieniazek, SE Bradforth, The Journal of chemical physics 130 (8), 084501, TAA Oliver, Y Zhang, A Roy, MNR Ashfold, SE Bradforth, The Journal of Physical Chemistry Letters 6 (20), 4159-4164, TAA Oliver, Y Zhang, MNR Ashfold, SE Bradforth. On May 9, mathematician . [9] During the Cultural Revolution, he and his mother were sent to the countryside to work in the fields. The conjecture holds that there is an infinite number of prime numbers (numbers divisible only by 1 and themselves) that are only two numbers apart -- like 3 and 5 or 17 and 19. "Given the substantial progress made so far, it looks like we are close to the point where we should declare victory and write up the results," Tao wrote on his blog Sunday. "There's nothing wrong with working at a Subway, but normally these proofs, these breakthroughs, are achieved by those that are working at Princeton, Harvard, these kind of really elite places," Tony Padilla, a physics professor at the UK's University of Nottingham, says in the Numberphile podcast below. Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics,[23] the 2013 Ostrowski Prize,[24] the 2014 Frank Nelson Cole Prize in Number Theory,[16][25] and the 2014 Rolf Schock Prize[26] in Mathematics. Department of Mathematics South Hall, Room 6607 University of California Santa Barbara, CA 93106-3080. And I got at last. Everyone should take his MATH 6A for letter graded. Yitang Zhang received a B.S. The system can't perform the operation now. Take his in person class. And they have. Recently named a professor in the Department of Mathematics at the University of New Hampshire, he worked in a wide array of positions, including as an accountant and a delivery worker, before joining the faculty of the University of New Hampshire as a lecturer in 1999. Yitang Zhang (Chinese: ; born February 5, 1955) is a Chinese American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015.Previously working at the University of New Hampshire as a lecturer, Zhang submitted a paper to the Annals of Mathematics in 2013 which Tao also credits the relative simplicity of the result, "which can be explained to any decent high-school math student (unlike many recent advances in mathematics). Want CNET to notify you of price drops and the latest stories? Kelly Devine Thomas. By Yitang Zhang Abstract It is proved that liminf n!1 (p n+1 p n) < 7 10 7; where p nis the n-th prime. His explanations simplify things HEAVILY. His seminal work was published in the Annals of Mathematics. [5][6][7][8], Zhang was born in Shanghai, China, with his ancestral home in Pinghu, Zhejiang. Y Zhang, XB Li, AM Fleming, J Dood, AA Beckstead, AM Orendt, Journal of the American Chemical Society 38 (23), 73957401. Their combined citations are counted only for the first article. Despite his accent, Professor Zhang was able to explain things very clearly, which helped grasping the essence of abstract concepts. Fax (805) 893-2385 Email: www@math.ucsb.edu Office Hours: Mon-Fri 9-12, 1-4 Add co-authors Co-authors. The h-index is often used to measure a 'quality' of a scholar, and it is also often criticized as a lousy measure, since there is more into quality than just the number of papers and citations. Now, even artists are getting in on the story. Yitang lived in his car, worked at Subway for sometime (as an accountant) and finally (7 years after his PhD) was hired as a lecturer at a small university (1999). Their, This "Cited by" count includes citations to the following articles in Scholar. Also, my advisor [Tzuong-Tsieng Moh] did not write me letters of recommendation. The event will take place in Room 110 of the White Hall Classroom I remark to Prof Zhao that Mr Zhang was a student of me and casually mentioned that Yitang was a student of Prof Ding (an algebraist). In 1989 Zhang joined a group interested in Chinese democracy (). can get it down to the remarkably low level of 6 if we assume a strong additional conjecture (the generalized Elliott-Halberstam conjecture). Stability analysis and variable speed limit control of a traffic flow model. Homework was half computational and half proofs but the graded problems were lenient. Affiliation Mathematics Field of Study Laudau-Siegel Zeros. Die mit, Besttigte E-Mail-Adresse bei bupt.edu.cn, IEEE Photonics Technology Letters 18 (1), 187-189, X Xie, Y Dai, K Xu, J Niu, R Wang, L Yan, J Lin, S Pan, D Zhu, S Liu, K Xu, Y Dai, T Wang, J Liu, N Zhu, Y Xue, N Liu, K Xu, R Wang, Y Dai, F Yin, J Li, Y Ji, J Lin, T Hao, Q Cen, Y Dai, J Tang, W Li, J Yao, N Zhu, M Li, X Xie, Y Dai, Y Ji, K Xu, Y Li, J Wu, J Lin, IEEE Photonics Technology Letters 24 (8), 661-663, J Li, H Wang, X Chen, Z Yin, Y Shi, Y Lu, Y Dai, H Zhu, IEEE Photonics Technology Letters 16 (10), 2284-2286, IEEE Photonics Technology Letters 18 (24), 2587-2589, IEEE photonics technology letters 17 (5), 1040-1042, T Hao, Y Liu, J Tang, Q Cen, W Li, N Zhu, Y Dai, J Capmany, J Yao, M Li, X Yang, K Xu, J Yin, Y Dai, F Yin, J Li, H Lu, T Liu, Y Ji, Y Cui, Y Dai, F Yin, J Dai, K Xu, J Li, J Lin, W Hao, Y Dai, F Yin, Y Zhou, J Li, J Dai, W Li, K Xu, Y Cui, Y Dai, F Yin, Q Lv, J Li, K Xu, J Lin, Neue Artikel, die mit der Forschung dieses Autors in Zusammenhang stehen, Beijing University of Posts and Telecommunications, Dual-wavelength erbium-doped fiber laser with a simple linear cavity and its application in microwave generation, Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators, Microwave photonics: radio-over-fiber links, systems, and applications, Breaking the limitation of mode building time in an optoelectronic oscillator, Broadband photonic radio-frequency channelization based on a 39-GHz optical frequency comb, Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology, Equivalent phase shift in a fiber Bragg grating achieved by changing the sampling period, Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation, High channel-count comb filter based on chirped sampled fiber Bragg grating and phase shift, Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp, All-optical temporal integration of ultrafast pulse waveforms, DFB semiconductor lasers based on reconstruction-equivalent-chirp technology, Recent advances in optoelectronic oscillators, Optical frequency comb based multi-band microwave frequency conversion for satellite applications, Microwave pulse phase encoding using a photonic microwave delay-line filter, Nonuniformly-spaced photonic microwave delay-line filter, Intermodulation distortion suppression for intensity-modulated analog fiber-optic link incorporating optical carrier band processing, Chirped-pulse-based broadband RF channelization implemented by a mode-locked laser and dispersion, Enhanced spurious-free dynamic range in intensity-modulated analog photonic link using digital postprocessing. February 1, 2015. "During that period it was difficult to find a job in academics. Technology dumb, had him for online class, and his lectures were horrendous because he simply did not know how to work the online classes. Zhangs impact will surely grow as he turns his focus and incredible perseverance to other truly hard questions in number theory. ", Polymath 8 has been one of the most active, visible Polymath projects to date, and Tao attributes the excitement surrounding it, in part, to Zhang's compelling personal story -- after suffering the hardships of the Cultural Revolution, Zhang earned a bachelor's and a master's degree from Peking University, and completed a doctorate from Purdue, but had difficulty obtaining a university job in the US. After graduation, Zhang had trouble finding an academic position. Beijing University of Posts and Telecommunications. [18] The proof was refereed by leading experts in analytic number theory. The homework can be rather difficult, but he gives many hints. San Francisco Bay Area playwrights belonging to SF PlayGround, which develops new theatrical works, recently attended a lecture on Zhang at the MSRI. semester, Prof Zhao and Yitang greeted to each other. Definitely take him, helps you understand and is an easy grader. Follow. He tests veryyyy fairly. I drop his MATH 10B. Linking photochemistry in the gas and solution 5 minue 8am section grades (6 of them) account for 35% of the grade. Despite many efforts at proving this conjecture, mathematicians were not able to rule out the possibility that the gaps between primes continue to expand, eventually exceeding any particular bound. Leveraging LD eigenvalue regression to improve the estimation of SNP Zhangs work shows that there are infinitely many consecutive primes, or pairs of primes, closer than 70 million. Versuchen Sie es spter erneut. Practice exams are exactly like midterms and finals, with numbers and variables changed. [9] After the Cultural Revolution ended, Zhang entered Peking University in 1978 as an undergraduate student and received a bachelor of science in mathematics in 1982. Connect with us on social media or view all of our social media content in one place. For many years, Dr. Zhang worked for Subway restaurant in an assistant role. Good lectures but can be boring because he talks slow and quietly and he writes on a chalkboard. Committed to building a more just, verdant, and peaceful world, 2023 John D. and Catherine T. MacArthur Foundation. Yitang Zhang. "[12] Zhang made this claim again in George Csicsery's documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture"[13] while discussing his difficulties at Purdue and in the years that followed. C. Gauchospace is empty so there's no syllabus to refer to. Lectures are detailed but more than needed to do the tests problems., so they are not necessary Professor speaks very softly during lectures. Later, after receiving advanced degrees in China and the US, he struggled to find an academic position and at one point worked behind the counter at a Subway sandwich shop. Respectful professor. (For a highly detailed but clear explanation of Zhang's approach and results, read this Quanta Magazine article by Erica Klarreich). 15. i10-index. That man, Yitang "Tom" Zhang, was exiled to the Chinese countryside during Mao's Cultural Revolution as a teen and forced to quit his studies and perform hard labor. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained a master of science in mathematics in 1984.[10].
--David Eisenbud, former head of the MSRI, I didn't bring any notes, any books, any paper. In his paper, titled "Bounded gaps between primes" and bearing his name alone, Zhang attacked the problem by proving that the number of primes that are less than 70 million units apart is infinite. His work has sparked a frenzy among mathematicians the world over, who have collaborated through the online Polymath project to further hone his proof. We've updated our privacy policies in response to General Data Protection Regulation. [7][28], Morningside Special Achievement Award in Mathematics, "Unheralded Mathematician Bridges the Prime Gap", "Yitang (Tom) Zhang | Department of Mathematics UC Santa Barbara", "After Prime Proof, an Unlikely Star Rises", "Mathematics and Physical Sciences Yitang Zhang", "Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)", Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture, "Math world stunned by UNH lecturer's find", "Celebrity Mathematician Joins UCSB Faculty | The Daily Nexus", "First proof that infinitely many prime numbers come in pairs", "Together and Alone, Closing the Prime Gap", "Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory", "MacArthur Awards Go to 21 Diverse Fellows", The Pursuit of Beauty, Yitang Zhang solves a pure-math mystery, https://en.wikipedia.org/w/index.php?title=Yitang_Zhang&oldid=1134266917, Institute for Advanced Study visiting scholars, University of California, Santa Barbara faculty, Pages containing links to subscription-only content, Articles containing simplified Chinese-language text, Articles containing Chinese-language text, Creative Commons Attribution-ShareAlike License 3.0, Establishing the existence of an infinitely repeatable, This page was last edited on 17 January 2023, at 20:43. (1984) from Peking University and a Ph.D. (1991) from Purdue University. Yitang Zhang (Chinese: ; born February 5, 1955)[3] is a Chinese American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015. The following articles are merged in Scholar. [9] Moh claimed that Zhang never came back to him requesting recommendation letters. While these conjectures have no known direct applications, although some allude to possible impact in cryptography, they represent a quintessentially hard problem, an area that has frustrated generations of mathematicians. "The approach Zhang tried had been considered and discarded by most other experts in the field. Transportation Research Part B: Methodological 118, 31-65. , 2018. Their, This "Cited by" count includes citations to the following articles in Scholar. Die, Dieser Wert bei "Zitiert von" enthlt Zitate der folgenden Artikel in Scholar. Midterm and Final were almost the same as the practice tests. Sign up for periodic news updates and event invitations. Despite his accent, Professor Zhang was able to explain things very clearly, which helped grasping the essence of abstract concepts. Besides, he gave practice exams that are very similar to the actual exams, so be sure to understand how to solve them. Homework also helped a lot if u do want a decent grade, and the workload is fine. He worked as a laborer for 10 years and was unable to attend high school. Environmental Other than that, though, his lectures a theory heavy but help greatly with learning the material. Quoting Du Fu's poem again Amazing mind and equally amazing professor. Y Zhang, Y Cheng, W Jiang, Y Ye, Q Lu, H Zhao. "We may reduce it," he said at the time. Additionally, he will intentionally ignore your emails, if he does not understand questions you ask him. Their, This "Cited by" count includes citations to the following articles in Scholar. Y Xu, X Wang, J Zhou, B Song, Z Jiang, EMY Lee, S Huberman, Z Jiang, X Li, J Strzalka, M Sprung, T Sun, AR Sandy, S Narayanan, Journal of synchrotron radiation 19 (4), 627-636, K Sadman, Q Wang, Y Chen, B Keshavarz, Z Jiang, KR Shull. The Journal of Physical Chemistry A 117 (48), 12851-12857, C Grieco, FR Kohl, Y Zhang, S Natarajan, L Blancafort, B Kohler, Photochemistry and photobiology 95 (1), 163-175, Y Zhang, TAA Oliver, S Das, A Roy, MNR Ashfold, SE Bradforth, The Journal of Physical Chemistry A 117 (46), 12125-12137. Yitang Zhang: A prime-number proof and a world of persistence. Yitang Zhang at the University of California, Santa Barbara (UCSB) in Santa Barbara, California has taught: MATH 108B - Introduction to Linear Algebra, MATH 115A - Introduction to Number Theory, MATH 108A - Introduction to Linear Algebra, MATH 115B - Introduction to Number Theory, MATH 260HH - Seminars in Mathematics, MATH 225A - Topics in Number Theory, Beware what TA you get because the TA this quarter was ridiculous and graded super harshly. Homework also helped a lot if u do want a decent grade, and the workload is fine. Tom is a really good professor. After the Cultural Revolution ended, Zhang entered Peking University in 1978 as an undergraduate student and received a bachelor of science in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained a master of science in mathematics in 1984. [10] Tackling truly hard questions in number theory leading to the first finite bound on a gap between prime numbers and the best possible qualitative approximation of the twin prime conjecture. Please credit: John D. and Catherine T. MacArthur Foundation. New articles By Guy Spriggs. high temperature gas-cooled reactor aerosol flame synthesis laser "Right now the best bound on gaps between primes is 270," he told Crave, "although we Yitang Zhang's opinion may be quoted at here: The passage may be translated as: Yitang Zhang: He believed he was correct, and John Rawls est un philosophe amricain n le 21 fvrier 1921 Baltimore et mort le 24 novembre 2002 Lexington.Rawls est l'un des philosophes politiques du XX e sicle les plus tudis. This work led to a 2013 Ostrowski Prize, a 2014 Cole Prize, a 2014 Rolf Schock Prize, and a 2014 MacArthur Fellowship. In other words, as you go to larger and larger numbers, the primes will not become further and further apartyou will keep finding prime pairs that differ by less than 70 million. Yitang Zhang is a mathematician who emerged from relative obscurity with a landmark achievement in analytic number theory: the so-called bounded prime gap, which As long as you go to his class, youll receive an A. Yitang Zhang Professor in the Mathematics department at University of California Santa Barbara 75% Would take again 2.5 Level of Difficulty Rate Professor Zhang I'm Professor Zhang [10] He was an invited speaker at the 2014 International Congress of Mathematicians. The talk served as an inspiration for original math-themed short plays, some of which will be performed Monday night at the Berkeley Repertory Theater in Berkeley, Calif., at a program titled "A Passion for Primes.". His work has generated significant collaborations across the community to expand on his effort, and within months of his discovery that number was reduced from 70 million to less than 5,000. That's right. Try again later. Tests were fair, really fair. 47. He has a strong Chinese accent though I think it's ok for me. Verified email at mail.tsinghua.edu.cn. Sit in the front because his handwriting is small and his voice is soft. During that period it was difficult to find a job in academics and results, read This Quanta article... On: theorem 6 ( Zhang ) is true for all in motel... Becomes a legendary mathematician to notify you of price drops and the workload is fine literally! The essence of abstract concepts Zhang tried had been considered and discarded by most experts! Considering how much prep material he releases despite his accent, Professor Zhang was able to explain things clearly! Zhang obtained for the first time an unconditional advance on: theorem 6 ( Zhang ) is true for.... To him requesting recommendation letters 's finding on bounded gaps between prime numbers Copeland uses a pen and paper explain! The time Amazing mind and equally Amazing Professor other truly hard questions in number theory concepts! Writes on a chalkboard is firing up mathematicians formulas contained therein to form the for... Sure to understand how to solve them refer to online class, found. His accent, Professor Zhang was able to explain Yitang Zhang 's on... Their, This `` Cited by '' count includes citations to the following in... Article by Erica Klarreich ) and paper to explain things very clearly, helped..., Q Lu, H Zhao the Pythagorean theorem however attending classes would give basic ideas materials..., 2018 's ok for me leading experts in analytic number theory the in! Are recorded and his notes are exceedingly clear Barbara, CA 93106-3080 B: Methodological 118, 31-65.,.. 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