{"product_id":"ai-and-mathematical-tools","title":"Essential Math Tools for AI: A Practical Refresher","description":"\u003cp id=\"isPasted\" style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eCourse Description \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eThis course will make some of the necessary mathematical background for AI accessible by decomposing and illustrating difficult concepts with a number of real-world examples and problems for students to work out. Namely, the course consists of five modules:\u003c\/p\u003e\n\u003cul\u003e\n\u003cli style=\"box-sizing: border-box;\"\u003eLinear Algebra\u003c\/li\u003e\n\u003cli style=\"box-sizing: border-box;\"\u003eBasic Graph Theory\u003c\/li\u003e\n\u003cli style=\"box-sizing: border-box;\"\u003eBasic Control Theory\u003c\/li\u003e\n\u003cli style=\"box-sizing: border-box;\"\u003eProbability\u003c\/li\u003e\n\u003cli style=\"box-sizing: border-box;\"\u003eOptimization\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eThe course will help provide students with an introductory overview and refresher on the above topics, thereby preparing them for advanced courses in machine learning, AI, cyber-physical systems data science, and autonomous systems, among others.\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eBelow is the course schedule. It is recommended that you work through one module per week. The entire course is estimated to take 15 hours to complete. Each module is estimated to take 15 hours to complete. Note: \u003cu style=\"box-sizing: border-box;\"\u003eQuizzes are mandatory, the next module will\u003c\/u\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003e\u003cu style=\"box-sizing: border-box;\"\u003e not\u003c\/u\u003e\u003c\/strong\u003e\u003cu style=\"box-sizing: border-box;\"\u003e appear until you have successfully completed the previous module and achieved an 80% or higher on the quiz.\u003c\/u\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eThis is an asynchronous, self-paced course with no live instructor. The flexible schedule allows learners to complete coursework and assignments at their own pace and time. \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\u003cstrong\u003eNote: You will receive a completion certificate from Purdue upon completing the course modules with an 80% or higher grade.\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eLearning Outcomes\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eAt the end of this course, you should be able to:\u003c\/p\u003e\n\u003cul\u003e\n\u003cli style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003eAnalyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence, and eigenvalues\u003c\/li\u003e\n\u003cli style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003eDefine graph properties such as diameter, degrees, and connectivity, and apply them to analyze networked systems.\u003c\/li\u003e\n\u003cli style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003eDefine properties of linear systems, including controllability, observability, and stability, and apply them to design state estimators and feedback controllers.\u003c\/li\u003e\n\u003cli style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003eDefine probability distributions and moments of random variables and characterize the long-term behavior of stochastic processes.\u003c\/li\u003e\n\u003cli style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003eSpecify the fundamental optimality conditions for optimization problems and implement basic algorithms to find the optimizers.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp style=\"background-color: white; box-sizing: border-box; color: rgb(65, 65, 65);\"\u003e \u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eCourse Schedule and Duration\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eBelow is the course schedule. It is recommended that you work through one module per week. The entire course is estimated to take 15 hours to complete. Each module is estimated to take 15-18 hours to complete. Note: \u003cu style=\"box-sizing: border-box;\"\u003eQuizzes are mandatory, and assignments and discussions are optional. \u003c\/u\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eTarget Audience\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp style=\"-webkit-text-stroke-width: 0px; background-color: white; box-sizing: border-box; color: rgb(65, 65, 65); font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; margin-top: 0px; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003eSales engineers\/business development executives, college students, and anyone interested in learning more about AI and mathematical tools. \u003c\/p\u003e\n\u003cfigure class=\"table\"\u003e\n\u003ctable cellpadding=\"0\" cellspacing=\"0\" border=\"1\" style=\"-webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); border-collapse: collapse; box-sizing: border-box; color: rgb(65, 65, 65); empty-cells: show; font-family: sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; max-width: 100%; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-decoration-thickness: initial; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;\"\u003e\n\u003ctbody style=\"box-sizing: border-box;\"\u003e\n\u003ctr style=\"box-sizing: border-box; height: 16.15pt;\"\u003e\n\u003ctd width=\"138\" style=\"border: 1pt solid windowtext; box-sizing: border-box; height: 16.15pt; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eModule\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top: 1pt solid windowtext; box-sizing: border-box; height: 16.15pt; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e\u003cstrong style=\"box-sizing: border-box;\"\u003eTopic \u0026amp; Readings\u003c\/strong\u003e\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr style=\"box-sizing: border-box;\"\u003e\n\u003ctd width=\"138\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e1\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eVectors \u0026amp; Matrices\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eSystem of Equations and Eigenvalues\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eDiagonalization \u0026amp; Definite Matrices\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eNorms\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr style=\"box-sizing: border-box;\"\u003e\n\u003ctd width=\"138\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e2\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eBasics \u0026amp; Graph Properties\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eSearch Algorithms \u0026amp; Trees\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eShortest Paths\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr style=\"box-sizing: border-box;\"\u003e\n\u003ctd width=\"138\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e3\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eBasics \u0026amp; Stability\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eControllability \u0026amp; Observability\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eLyapunov Theory\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr style=\"box-sizing: border-box;\"\u003e\n\u003ctd width=\"138\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e4\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eBasics \u0026amp; Conditional Probability\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eRandom Variable and Expectations\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eMarkov Chains\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr style=\"box-sizing: border-box;\"\u003e\n\u003ctd width=\"138\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 103.25pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003e5\u003c\/p\u003e\n\u003c\/td\u003e\n\u003ctd width=\"372\" style=\"border-bottom: 1pt solid windowtext; border-image: initial; border-left-style: none; border-right: 1pt solid windowtext; border-top-style: none; box-sizing: border-box; min-width: 5px; padding: 0in 5.4pt; user-select: text; vertical-align: top; width: 279pt;\"\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eExtreme \u0026amp; Optimality\u003c\/p\u003e\n\u003cp style=\"box-sizing: border-box; margin-top: 0px;\"\u003eInfimum \u0026amp; Supremum\u003c\/p\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/tbody\u003e\n\u003c\/table\u003e\n\u003c\/figure\u003e","brand":"Purdue University","offers":[{"title":"Default Title","offer_id":43106835038275,"sku":"18235","price":21300.0,"currency_code":"JPY","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0567\/3402\/3747\/files\/800x800_Purdue_AIAndMathematicalTools.png?v=1776700945","url":"https:\/\/store-dev2.semi.org\/en-jp\/products\/ai-and-mathematical-tools","provider":"SEMI Dev 2","version":"1.0","type":"link"}