[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-292078-105":59,"doc-detail-292078-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","qualifying-exam-syllabus-qualifying-exam-syllabus-izzy-detherage","Qualifying Exam Syllabus - Qualifying Exam Syllabus Izzy Detherage","","Qualifying Exam Syllabus for Izzy Detherage lists the committee members and the exam date, December 1, 2023. The syllabus is organized into three study areas: Spectral Graph Theory (including Laplacians, expander graphs, potential theory, and associated inequalities and theorems), Probability Theory (measure and convergence tools, characteristic functions and CLT, martingales and conditioning, and Markov chains with spectral and cutoff themes), and Analysis of Boolean Functions (Fourier expansion, social choice and influences, majority and threshold functions, noise stability, and hypercontractivity).",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/qualifying-exam-syllabus-qualifying-exam-syllabus-izzy-detherage/292078/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/qualifying-exam-syllabus-qualifying-exam-syllabus-izzy-detherage/292078.png","ImageObject",300,407,{"name":92,"@type":93},"wps_ap_test_251126_0180","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the exam date for Izzy Detherage’s qualifying exam?","Question",{"text":113,"@type":114},"The exam date is December 1, 2023.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the major topics covered besides the minor topic?",{"text":118,"@type":114},"The syllabus has two major topics: Spectral Graph Theory and Probability Theory, plus one minor topic on Analysis of Boolean Functions.",{"name":120,"@type":111,"acceptedAnswer":121},"Which subjects are included in the Probability Theory part of the syllabus?",{"text":122,"@type":114},"It covers measure theory foundations, random sequences and series, characteristic functions and the central limit theorem, martingales and conditioning, and Markov chains including spectral-related topics, coupling, and cutoff.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},292078,1789647999,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":81},8796095027276,"https://avatar.qwps.com/avatar/d3BzX2FwX3Rlc3RfMjUxMTI2XzAxODA=","Qualifying Exam Syllabus Izzy Detherage  \nCommittee: Nikhil Srivastava, Shirshendu Ganguly, Avishay Tal, Venkat Guruswami  \nExam Date: December 1, 2023  \n1. Major Topic: Spectral Graph Theory  \nLinear Algebra Preliminaries. (Spielman 2, 4) spectral theorem, Rayleigh quotients, CourantFischer, positive (semi-)definiteness, Perron-Frobenius, eigenvalue interlacing  \nLaplacians. (Trevisan 3-5, Williamson 5-7) standard / normalized Laplacian, eigenvalues and connectivity / cuts, matrix-tree theorem, edge expansion and conductance, Cheeger’s Inequality Sparse Cut Problems. (Trevisan 10-15, Matousek 4.2-4.3, Rothvoss) uniform and nonuniform sparsity, Leighton-Rao, Bourgain’s theorem, Geomans-Linial/ARV  \nExpander Graphs. (Trevisan 16-21) characters, Cayley graphs of Abelian groups, Zig-Zag product, Marguli-Gabber-Galil Expanders, quasirandomness, random walks on expanders Potential Theory. (Spielman 10-13) random walks on graphs, spring and resistor networks, effective resistance, Schur complements, random spanning trees  \n2. Major Topic: Probability Theory  \nMeasure Theory. (Durrett 1,2) σ-algebras, Caratheodory’s extension theorem, DCT, MCT, Fatou’s lemma, monotone class lemma, Fubini’s theorem, independence, Borel-Cantelli lemmas Random Sequence and Series. (Durrett 2) modes of convergence, WLLN, SLLN, GlivenkoCantelli, Portmanteau, Helly’s selection theorem, tightness  \nCharacteristic Functions and Central Limit Theorem. (Durrett 3) inversion formula, uniqueness and continuity, central limit theorem for iid sequence, Lindeberg-Feller CLT, Poisson convergence theorem  \nMartingales and Conditioning. (Durrett 4) Lebesgue-Radon-Nikodym theorem, conditional expectation, filtrations, stopping times, martingales, uniform integrability  \nMarkov Chains. (LPW 4.3, 5, 1.6, 12.1-12.4, 13.1-13.3, 18.1-18.3, 20) asymptotic convergence, coupling, Wasserstein distance, reversibility, topics relating to spectra, cutoff, continuous-time Markov chains  \n3. Minor Topic: Analysis of Boolean Functions  \nFourier expansion. (O’Donnell 1) orthonormal basis of parity functions, basic Fourier formulas, probability densities, convolution, almost linear functions, BLR test  \nBasic concepts and social choice. (O’Donnell 2.1-2.3) social choice functions, influences and derivatives, total influence  \nMajority and threshold functions. (O’Donnell 5.1, 5.2, 5.5) linear threshold functions, polynomial threshold functions, majority, CLT, Peres’s theorem, uniform noise stability Hypercontractivity. (O’Donnell 9.1, 9.6) Bonami’s lemma, Kahn, Kalai, Linial theorem, Friedgut’s Junta lemma","cbCaicGHcoACnDvx","https://ap.wps.com/l/cbCaicGHcoACnDvx","pdf",84776,"English","# Major Topic: Spectral Graph Theory\n## Major Topic: Probability Theory\n## Minor Topic: Analysis of Boolean Functions","[{\"question\":\"What is the exam date for Izzy Detherage’s qualifying exam?\",\"answer\":\"The exam date is December 1, 2023.\"},{\"question\":\"What are the major topics covered besides the minor topic?\",\"answer\":\"The syllabus has two major topics: Spectral Graph Theory and Probability Theory, plus one minor topic on Analysis of Boolean Functions.\"},{\"question\":\"Which subjects are included in the Probability Theory part of the syllabus?\",\"answer\":\"It covers measure theory foundations, random sequences and series, characteristic functions and the central limit theorem, martingales and conditioning, and Markov chains including spectral-related topics, coupling, and cutoff.\"}]","Qualifying Exam Syllabus - Qualifying Exam Syllabus Izzy Detherage | PDF"]