PPT-Linear sketching for Functions over Boolean Hypercube

Grigory Yaroslavtsev Indiana University Bloomington httpgrigoryus with Sampath Kannan U Pennsylvania Elchanan Mossel MIT and Swagato Sanyal NUS Sketching. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations . can. not . be. . seen. Rainer Kaenders. University . of. Cologne. GeoGebra Conference Linz 2011. Functions. . can. not . be. . seen. … but . can. . be. . represented. . GeoGebra . can. . Holt Algebra I. – 5.1. LT: F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.. Warm-Up. Wednesday, 04 February 2015. Solve 2. x. – 3. M. AL- . Towaileb. 1. Boolean Functions. In Boolean algebra we work with the . set {0,1}. , . where:. 0 ≡ F . (False) & . 1 ≡ T . (True).. The 3 Operations used in Boolean Algebra are:. Complementation ( . David Plaxco. Linear Independence of Functions. Definition of linear independence of vector-valued functions. :. Let . f. i. : . I . = (. a,b. ) . → . . . n. , . I = 1, 2. ,…. , n. .. . The . Efficient Algorithms for Low-Sensitivity Functions. Rocco Servedio. Joint work with . Parikshit. . Gopalan. (MSR). Noam Nisan (MSR / Hebrew University). Kunal. . Talwar. (Google). Avi. . Wigderson. of Depth-Three and . Arithmetic Circuits with General Gates. Oded. . Goldreich. Weizmann Institute of Science. Based on Joint work with . Avi. . Wigderson. Original title. : . “On . the Size of Depth-Three Boolean Circuits for Computing . L Al-. zaid. Math1101. 1. Boolean Functions. In Boolean algebra we work with the . set {0,1}. , . where:. 0 ≡ F . (False) & . 1 ≡ T . (True).. The 3 Operations used in Boolean Algebra are:. Define appropriate quantities from a situation, choose and interpret the scale and the origin for the graph, and graph the piecewise linear function.. Learning Goal . 2 . (HS.N-Q.A.1, 2, 3):. The student will be able to use units to solve multi-step contextual problems. 4. 3. 2. 1. 0. In addition to level 3.0 and beyond what was taught in class, the student may: . Make connection with other concepts in math.. Make connection with other content areas..  . The student will understand and explain the difference between functions and non-functions using graphs, equations, and tables.. Differentiate between linear and exponential functions.. 4. 3. 2. 1. 0. In addition to level 3, students make connections to other content areas and/or contextual situations outside of math..  . Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model.. Define appropriate quantities from a situation, choose and interpret the scale and the origin for the graph, and graph the piecewise linear function.. Learning Goal . 2 . (HS.N-Q.A.1, 2, 3):. The student will be able to use units to solve multi-step contextual problems. Lecture 5. Announcements. Homework 1 solutions are on Canvas. Homework 2 due on Thursday. Coming up: First midterm on Sept. 30. Agenda. Last time:. Boolean Algebra axioms and theorems (3.1,3.2). Canonical Forms (3.5). Differentiate between linear and exponential functions.. 4. 3. 2. 1. 0. In addition to level 3, students make connections to other content areas and/or contextual situations outside of math..  . Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model..