Math Lecture Notes

It has been published in 2006 by the AMS as volume 2 of the Clay Monographs in Math series. Mathematical Epidemiology (Lecture Notes in Mathematics (1945)) by Fred Brauer "Excellent survey of disease models" - by J. They are here for the use of anyone interested in such material. Psalm27:1 These are lecture notes for the Number Theory course taught at CMU inFall2017andFall2018. LECTURE 1 Introduction The source of all great mathematics is the special case, the con-crete example. Advanced Mathematical Physics Notes PDF. The lecture notes are in Hebrew; if you already know logic, you can use this opportunity to learn. post-gazette. MATH 322 - Spring 2007 - Lecture Notes Chapter 13: Complex Numbers Sections 1 & 2. Series Monográficas: Berkeley mathematics lecture notes. Notes on Alexandrian Greek mathematics. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. Revised and retyped in 2009 (pdf) 14. The first set of notes was drafted Fall 2005 and last edited in Spring 2011. The disjunction of A and B is true when either A or B (or both) are true; the disjunction is false when both A and B are false. e du/ ~ angenent/725 The T E X les a. With few. math 2 notes, Per SBE Rule, students must achieve four high school level units of math in order to graduate with a high school diploma, including Algebra I, Algebra II, and Geometry (or the equivalent courses, Integrated Math I, II, and III) and one additional mathematics course beyond Algebra I. Topics covered are Three Dimensional Space, Limits of functions of multiple variables, Partial Derivatives, Directional Derivatives, Identifying Relative and Absolute Extrema of functions of multiple variables, Lagrange Multipliers, Double (Cartesian and Polar coordinates) and Triple Integrals. Math 407 Class Lectures. Our legendary Head Start Lectures, delivered by elite past students, can give you a huge advantage going into class in 2021. of pages in this PDF lecture notes and the PDF file can be easily downloaded below. Lecture Notes: The files posted below are lecture notes from some previous courses that I've taught. MA 161 (Spring 2020), lecture notes are here due to the shift to online classes, the videos for lessons 22-35 are here MA 162 (Fall 2019), lecture notes are here MA 303 (Summer 2019), lecture notes are here (Summer 2017 (old 303) notes are here) MA 161 (Spring 2019), lecture notes are here MA 265 (Summer 2018), lecture notes are here. in Mathematics is mostly of two academic years but it may vary from institute to institute. Part A Guide to Part A courses Schedule of units for course: Part A Mathematics 2020-21. 1-D Kinematics. Lecture Notes from the Special Year on New Connections of Representation Theory to Algebraic Geometry and Physics. Please send any queries to [email protected] Mustafa Jarrar: Lecture Notes in Discrete Mathematics. Math Math. These are lecture notes from the course I taught at Berkeley, Fall 2008. Iterative Methods for Linear Systems. These notes for a graduate course in set theory are on their way to be-coming a book. Course lecture notes. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. Mathematics as a subject is vast and with these online tutorials, we have tried to segregate some major topics into distinct lectures. Lecture notes for Physics 10154: General Physics I fact, mathematics is simply an alternative short-hand language that allows us to easily describe and predict. We have numbered the videos for quick reference so it's reasonably obvious that each subsequent video. Discrete Mathematics and CombinatoricsMath EducationGeometry and TopologyAlgebra and Algebraic GeometryProbability and StatisticsDifferential EquationsNumber TheoryMathematical PhysicsGeneral. Math 155, Lecture Notes- Bonds Name_____ Section 10. Now we look at maps between dual spaces. The first set of notes was drafted Fall 2005 and last edited in Spring 2011. Also, I realize the board is hard to read, so I've supplied some linked lecture notes in the tab above (they may not align perfectly with these lectures, since. Math 111 Lecture Notes Section 4. Printing and bringing a copy of the notes to class will allow you to spend less time trying to write down all of the information and more time understanding the material/problems. 1 and Section 1. Programme Semester Name of Subject Subject Code Download; 1: B. Still being revised! Bkly08; Real Blow up Three lectures at MSRI, August 2008. Mathematics: Standard Mathematics January 2021 Lecture Slides (online Added by kvella13 on 25/01/2021. I am particu-larly grateful to Maria Avdeeva, Mark Cerenzia, Xinyi Chen, Matthew de. has very important mathematical properties, but it is very difficult to provide a substantive definition. While technology has had a great impact on teaching and learning, many courses are still taught in lecture format. For example, exponential growth is a growth pattern that is. Notes for the entire course are available as a single pdf file (Courtesy of Jonathan A. Lecture Notes for Math 1000. View a list of the courses required for high school graduation. I will make corrections and modifications throughout the term. ANN ARBOR Literature MODULAR FORMS. Best change I ever made. 46: log likelihood = -367. These notes were created for use as primary reading material for the graduate course Math 205A: Complex Analysis at UC Davis. The first set of notes was drafted Fall 2005 and last edited in Spring 2011. Garsia and Ömer Eğecioğlu | Oct 7, 2020. Lecture Notes. A term paper on a topic of your choice; this paper may be used for credit in another course. This series reports on new developments in all areas of mathematics and their applications - quickly, informally and at a high level. The readers should consult the original books for a better pre-. Math 244 Lecture Notes Chapter 18: Confidence Intervals for 1-Proportion Overview: Today, we will look at how information about samples (statistics) can be used to make predictions about information about larger populations (parameters). By Alpha C. It presents the various elementary concepts about functions students will need to know in Calcu-lus. MA8351 DM Notes. Mega Lecture. connection with a fundamental mathematical result called the Binomial Theorem; you may also recall the related “Pascal’s Triangle”). These notes are for personal educational use only and are not to be published or redistributed. FSc Part (1) Maths. Harvard Mathematics Department : Home page. I will make corrections and modifications throughout the term. Let T : V !W be linear. Public Lectures & Events. pdf 10/4/2012; Lecture Notes/140A_Notes_Ver3. Tests that are put out by the College Board, such as the SAT, put to test students’ abilities to work through a wide variety of problems. 113--142 William Cherry Equidimensional Nevanlinna Theory on Coverings of $C^n$. Over the past decade, statistics have undergone drastic changes with the. The course is intended to equip the scholars with the mandatory mathematical skills Associate in Nursing d techniques that square measure essential for an engineering course. 09/26: Removed all mentions of the word "domain". The principal square root is the positive square root. These lecture videos are organized in an order that corresponds with the current book we are using for our Math2210, Calculus 3, courses (Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson). Lecture 01. Compare to other sites it provides quality CBSE class 8 maths notes. 47, aic = 738. The goal of this course was to. 1E-mail: [email protected] 655 is an introduction to the basic concepts of modern topology: metric spaces, topological spaces, connectedness, compactness, completeness, quotient spaces, manifolds, and classification of surfaces. Discrete Mathematics Lecture Notes Incomplete Preliminary Version Instructor: L aszl o Babai Last revision: June 22, 2003 Last update: October 24, 2003. 3 An aside on completion of inner product spaces. In ordinary language, for repeated powers multiply the powers. Foundations (기초) History of Math (수학사) Set Theory (집합론) - Banach-Tarski paradox (바나흐-타르스키 역설) PDF: TEX. The series is a joint effort of the AMS and the Center for Pure and Applied Mathematics at the University of California Berkley (UCB CPAM) (ISSN 1092-9371). 3 Algebraic Proofs 6. LECTURE NOTES. pdf: Lectures on Kähler geometry, Ricci curvature, and hyperkähler metrics, Lectures given at Tokyo Institute of Technology, Tokyo, Japan, Summer 2019. For more information, please check the instructions below. See full list on smartzworld. An alternate approach: Somewhere in the middle of my first math degree I basically stopped taking notes in lectures (maybe 1/2 page, or a few lines per lecture, just any "aha" moment, really). definition-only; script-generated and doesn't necessarily make sense), example sheets, and the source code. An Easier Road Through Medical University is Only One Click Away!. The newly cre­at­ed file has the fol­low­ing con­tents:. The members of a set are referred to as its elements. c is some arbitrary constant. Preface Dominus Illuminatio Mea. 1 About these notes This is a working set of lecture notes for the Part A Electromagnetism course, which is part of the mathematics syllabus at the University of Oxford. Definitions; Notes; Generating Random Numbers on the TI-82; Chapter 2 - Describing, Exploring, and Comparing Data. References to speciﬁc pages of the textbooks listed above are indicated in the notes as follows: R1(190) indicates “for more information see Reference 1, Page 190”. Math for Economists. 2 Christopher Gri n « 2010-2012 Licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3. TT20 Online Lecture List; MT20 Online Lecture List; See the Department Of Statistics for more details on their lectures. Feynman Lecture Notes The Feynman Lectures on Physics, original course handouts, 1961-63 The Feynman Lectures on Physics was based on a two-year introductory physics course that Richard Feynman taught at Caltech from 1961 to 1963; it was published in three volumes during the years 1963 to 1965, and used as the introductory physics textbook at. Mathematics – I(M1) Course Objectives: 1. 1 MATH 221 { 1st SEMESTER CALCULUS LECTURE NOTES VERSION 2. Lecture notes, I take when attending math courses 🖋 - prokls/math-lecture-notes. Boyarchenko: notes for the lecture "Modular categories and modular functors". Statistics I. As postscript all (ps). Math 566 > Lecture notes: Lecture notes. Isometries of Euclidean space, formulas for curvature of smooth regular curves. Sc Computer Science Lecture Notes Click here to Download: M. HT21 online lecture list. LECTURE NOTES ON PROBABILITY, STATISTICS AND LINEAR ALGEBRA C. Welcome to send me your comments (e. The Reddick Lecture; Colloquia; Brooke Benjamin Lecture; The Simonyi Lecture; Conferences. Title: Co-authors: Status: Download: Nonlinear Schrodinger Equations at Critical Regularity: R. Our mission is to produce new generations of mathematically proficient. Some Lecture Notes. Cumulative Type Structures 91 2. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. For x>0 we have 0cU = U00+ (1 )U; x>0: (5. gz, E) Lecture Notes on Groups and Geometry by Nils-Peter Skoruppa (ps. Free College Algebra Notes and Videos. Despite all good intentions, when we arrived in Tianjin in May of 1987 we each had only about a week's worth of lectures written up, and just rough notes for the rest. School of Mathematics | School of Mathematics. 1The trigonometric functions The Pythagorean trigonometric identity is sin2 x +cos2 x = 1, and the addition theorems are sin(x +y) = sin(x)cos(y)+cos(x)sin(y),. Lagrange Multipliers 65 6. Section 12. These are some notes of courses that I’m teaching or have taught in the Hebrew University. Further Calculus II. Math Camp Notes Lecture Notes (updated August 23, 2017) Lecture 1 (updated August 8, 2017) Lecture 2 (updated August 8, 2017) Lecture 3 (updated August 8, 2017). At the end of your notes for the day, draw a line crossing the page so you’ll have a very clear demarcation of each day’s notes. Discrete mathematics notes (Note: these aren't specifically for IB, but they're very thorough) Complete lecture notes; Videos. 35 to rent $52. Here are lecture notes (Module by Module) covering more or less the same syllabus as Modules 12 - 25: Differential Equations II. The estimation of parameters can be carried out for this model as follows > z = arima(rrbonds,order=c(1,1,0)) > z Call: arima(x = rrbonds, order = c(1, 1, 0)) Coefficients: ar1 0. Lecture Notes for Abstract Algebra I James S. COPYRIGHT NOTICE These lecture notes are copyrighted materials (© Martin Z. Introduction: Newton’s Law(s) In Newtonian physics, a particle of mass mmoves through three-dimensional space according to the law. MA8151 EM-1 Notes. To this end I suggest the. Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. Rule of Product Processes: If a process can be reduced to a sequence of two processes for which process one has m possible outcomes and process two. Sc Computer Science Lecture Notes Click here to Download: M. There are 76 no. Math 2210 | Calculus III These lecture videos are organized in an order that corresponds with the current book we are using for our Math2210, Calculus 3, courses we have included the "pre-notes" and "post-notes" which are the notes of the lecture before we did the problems and after we worked everything out during the lecture, respectively. Davis Paul Kirk Author address: Department of Mathematics, Indiana University, Blooming-ton, IN 47405 E-mail address: [email protected] Dold, Heidelberg and B. Richard Phillips Feynman ForMemRS (/ ˈ f aɪ n m ə n /; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, as well as his work in particle physics for which he proposed the parton model. National Centre for Mathematics. Static Electricity. The series is a joint effort of the AMS and the Center for Pure and Applied Mathematics at the University of California Berkley (UCB CPAM) (ISSN 1092-9371). Still being revised! Bkly08; Real Blow up Three lectures at MSRI, August 2008. Sc Electronics Lecture Notes. definition-only; script-generated and doesn't necessarily make sense), example sheets, and the source code. These notes are for personal educational use only and are not to be published or redistributed. Lecture Notes DERIVED CATEGORIES. We have numbered the videos for quick reference so it's reasonably obvious that each subsequent video. Activity: Lecture. You may occasionally nd it helpful to have access to other resources that give a more expanded and detailed presentation of various topics than is available in Lax’s book or in the lecture notes. Math_140B_Ver9. Paperback$54. Lecture Notes 4. It has been designed while having a user at university (or at school) in mind, for instance a lecturer who is using it for preparing her/his lecture or even for actual teaching (by writing on the device and projecting the screen content for the audience) or a student who is using it for. 2 to page 18 What is Mathematical Modeling? Steps of the Modeling Process Wednesday, February 3 (pdf of Notes pages 9-15) Includes Section 1. 1The trigonometric functions The Pythagorean trigonometric identity is sin2 x +cos2 x = 1, and the addition theorems are sin(x +y) = sin(x)cos(y)+cos(x)sin(y),. Newton's Laws. Collection of all Lecture Notes from the semester. Home; LIVE Classes; Our Tutors; Video Lectures. by Larry Green. ,) Lecture Notes-Free Download. You see, what gets trans-mitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. PROBABILITY THEORY 1 LECTURE NOTES JOHN PIKE These lecture notes were written for MATH 6710 at Cornell University in the allF semester of 2013. Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Mathematics Subject Classiﬁcation (2010): 55-XX; 05-XX; 52-XX; 06-XX. Advanced Mathematical Physics Notes PDF. The current 2020 revision (dated June 6, 2020) updates my earlier version of the notes from 2018. By Alpha C. They have not been published elsewhere, and, as works in progress, are subject to significant revision. 2 and Jaeger 4. Any significant changes after first posting will be noted below by the date. Functions will be revisited several times during the semester. 140A Lecture Notes Follow. Engineering Mathematics 1 – Chapter 1; Engineering Mathematics 1 – Chapter 2; Engineering Mathematics 1 – Chapter 3; Engineering Mathematics 1 – Chapter 4; Engineering Mathematics 1 – Chapter 5; Engineering Mathematics 1 – Chapter 6; Engineering Mathematics 1 – Chapter 7; Engineering. Programme Semester Name of Subject Subject Code Download; 1: B. Lecture Notes. 2Series and Convergence Usually, we study infinite sequences in order to study “infinite summations. M January 20. If you ﬁnd the course difﬁcult then you are advised to buy this book, read the corresponding sections straight after the lectures, and do extra exercises from it. The first set of notes was drafted Fall 2005 and last edited in Spring 2011. Complex numbers The equation x2 + 1 = 0 has no solutions, because for any real number xthe square x 2is nonnegative, and so x + 1 can never be less than 1. This includes the fields of fluid, solid and structuralmechanics, dynamics and control, and related. Lecture notes for Physics 10154: General Physics I fact, mathematics is simply an alternative short-hand language that allows us to easily describe and predict. Lecture notes files. Eckmann, Zürich. (MN-38) Edited by John Erik Fornaess. By Alpha C. Mathematical models in evolutionary genetics and computational genomics. 1 (a)Find the initial amount of bacteria. Introduction: Newton's Law(s) In Newtonian physics, a particle of mass mmoves through three-dimensional space according to the law. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. Advanced Calculus Lecture Notes for Mathematics. Students can receive credit for at most one of MATH 312 and MATH 313/513. Lecture Notes Topic Unit Notes Free Download; ENGINEERING MATHEMATICS DIFFERENTIAL CALCULUS Click here to Download: ENGINEERING MATHEMATICS FUNCTIONS OF SEVERAL VARIABLES. Algebra & Alg. Algebra 2 Lecture Notes. You may occasionally nd it helpful to have access to other resources that give a more expanded and detailed presentation of various topics than is available in Lax’s book or in the lecture notes. Lecture notes for a one-semester course on writing in Mathematical English. Riemann surfaces Riemann surfaces by Marcus Berg 3 years ago 12 minutes, 52 seconds. Mathematics as a subject is vast and with these online tutorials, we have tried to segregate some major topics into distinct lectures. The newly cre­at­ed file has the fol­low­ing con­tents:. Printing and bringing a copy of the notes to class will allow you to spend less time trying to write down all of the information and more time understanding the material/problems. Activity: Lecture. Methods of Applied Mathematics Lecture Notes William G. The course is intended to equip the scholars with the mandatory mathematical skills Associate in Nursing d techniques that square measure essential for an engineering course. Eigenvalue problems. Lectures on The Finite Element Method By Ph. It has been published in 2006 by the AMS as volume 2 of the Clay Monographs in Math series. I certainly don't have a problem with keeping up with lecturers. indd 3 11/4/09 1:57:55 PM. (MN-38) Edited by John Erik Fornaess. Comments: Lecture course given by R. A term paper on a topic of your choice; this paper may be used for credit in another course. The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research and teaching. Math 1050 Projects. Mathematics as a subject is vast and with these online tutorials, we have tried to segregate some major topics into distinct lectures. van den Driessc he 2 , and Jianhong W u 3 1 Department of Mathematics, Universit y of British Columbia. 4 Thelanguageoflogic. 1A Preview of Calculus the Area Problem Ex. pt or [email protected] Lecture Notes for MA 132 Foundations D. Logic 1 (80423) (still going on). Math 1050 Chapters 6 & 8. In this section w e dev elop the formal deÞnition of manifolds and construct man y examples. The lecture notes are provided by faculty and researchers affiliated with the university’s Mathematics Department and the Center for Pure and Applied Mathematics. Math 244 Lecture Notes Chapter 18: Confidence Intervals for 1-Proportion Overview: Today, we will look at how information about samples (statistics) can be used to make predictions about information about larger populations (parameters). Games and Duality 90 X. I do not come from a math or physics background and I find this to be a great resource for understanding your published papers. LECTURE NOTES ON INFORMATION THEORY Preface \There is a whole book of readymade, long and convincing, lav-ishly composed telegrams for all occasions. Lecture Notes in Discrete Mathematics Marcel B. The members of a set are referred to as its elements. ISBN 978-1-56698-657-1. Math Videos contains lecture notes and video lectures for students to veiw from home. These topics really made me panic : reducing fractions and subtracting exponents. Paperback $54. Very useful! Slides from lectures on LaTeX. 1 Mathematical Preliminaries 1. lecture notes in mathematics and numerous book collections from fictions to scientific research in any way. by Larry Green. MATH 1012 Lecture Notes 2 Topics covered in lecture 02: 1. In the sequence above, the first term is , the second term is , the third term is , # % ) and so forth, with each successive term being twice the previous term. Floris Takens made outstanding contributions to dynamical systems. There's videos, and a whole lot more! OCW is a free and open online publication of material from thousands of MIT courses, covering the entire MIT curriculum, ranging from the introductory to the most advanced graduate courses. Matrices III. Notes 138 Chapter 6. Used with permission. 2 Prerequisites. First note that for two non-negative numbers a;bit holds that ab 1 p ap+ 1 q bq: For p= q= 2 this is the familiar \arithmetic-geometric mean" inequality which follows since (a b)2 0. In the sequence above, the first term is , the second term is , the third term is , # % ) and so forth, with each successive term being twice the previous term. tex Lecture Notes for Phys 780 "Mathematical Physics" Vitaly A. Axiomatic Set Theory 92 3. tex in the di­rec­to­ry complex- analysis and mas­ter. springerlink. Eigenvalue problems. I usually update the course notes each time I teach. 2Series and Convergence Usually, we study infinite sequences in order to study “infinite summations. ,) Lecture Notes-Free Download. 1007/978-3-540-79814-9 Lecture Notes in Mathematics ISSN print. Bandeira, A. A Fitness Program for Science Students, Plenum Press, New York 1995. Further Calculus I. he previous examplesT also show that binomial coefficients possess a useful symmetry, namely, n k = n nk −. Any significant changes after first posting will be noted below by the date. I am currently referring Tao's lecture notes on complex analysis, but at many points he has referred to Wikepedia so everything is not covered there. Lecture Notes for Abstract Algebra I James S. This paper. They are aimed at the General Public, schools and anyone who just wants to come along and hear a bit more about what maths is really about. Comment goes here. I usually update the course notes each time I teach. Tests that are put out by the College Board, such as the SAT, put to test students’ abilities to work through a wide variety of problems. Sections covered by Exam 1: Sections covered by Exam 2: Sections covered by Exam 3: Remaining Sections: Last updated on 17 November 2020 rjh. Iterative Methods for Linear Systems. The timetables for all parts of the Mathematical Tripos and NST Mathematics are also available via https://www. The course is intended to equip the scholars with the mandatory mathematical skills Associate in Nursing d techniques that square measure essential for an engineering course. 2), as two approximations of the integral (assuming that the function. 8 Events are subsets of the sample space (A,B,C,). • Tuesday Jan 5, 2021 • Andras Vasy (Stanford University) 4:00pm I: The black hole stability problem — an introduction and results 5:00pm II: Analysis and geometry in the black hole stability problem • Prof. Cambridge Notes Below are the notes I took during lectures in Cambridge, as well as the example sheets. notation name O(1) constant O(log(n)) logarithmic O((log(n))c) polylogarithmic. Complex numbers The equation x2 + 1 = 0 has no solutions, because for any real number xthe square x 2is nonnegative, and so x + 1 can never be less than 1. accompanied by them is this computational approach to riemann surfaces lecture notes in mathematics that can be your partner. Shakarchi (Princeton Uni-. 9--55 Serge Lang Equidimensional higher dimensional theory. Download latex template for notes. Lecture Notes School Of Mathematics The University Of Merely said, the. LaTeX Symbols. Download with Google Download with Facebook. Lecture Notes 1. Lecture 7: Comparison and Math Operations: LECT07. Index of Math Terms. The set of all scalars is. Lecture Notes for Introductory Probability Janko Gravner Mathematics Department University of California Davis, CA 95616 gr[email protected] Mathematics is the study of quantity, structure, space, and change. Cynthia Church pro-duced the ﬁrst electronic copy in December 2002. A program in Quantum Field Theory for mathematicians was held at the Institute for Advanced study during the academic year 1996-97. for information about price, terms of payment etc. A fourth undergraduate program leads to the degree Bachelor's of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science. Boyarchenko: notes for the lecture "Modular categories and modular functors". Lecture Notes for Section 8. 3 to page 26 and Section 3. 3 An aside on completion of inner product spaces. Lecture 6: Rolle's Theorem, Mean Value Theorem: PDF: Lecture 7: Cauchy Mean Value Theorem, L'Hospital Rule: PDF: Lecture 8: Fixed Point Iteration Method, Newton's Method: PDF: Lecture 9: Sufficient Conditions for Local Maximum, Point of Inflection: PDF: Lecture 10: Taylor's Theorem: PDF: Lecture 11-13 : Infinite Series, Convergence Tests. Circular Motion and Satellite Motion. 2 Christopher Gri n « 2010-2012 Licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3. This course is the basic course in mathematical logic, presenting Gödel’s completeness theorem and related subjects. Basic Mathematics (Math 187) Beginning Algebra Part I (Math 152A) Beginning Algebra Part II (Math 152B) Intermediate Algebra (Math 154) Survey of Mathematics (Math 102) Elementary Statistics (Math 201) College Algebra Part I (Math 103A). Work and Energy. This is a home page for a course of 16 lectures to second year Cambridge mathematics students over 8 weeks. Its publisher is Springer Science+Business Media (formerly Springer-Verlag). Final Exam Review Material. Welcome to my math notes site. The Reddick Lecture; Colloquia; Brooke Benjamin Lecture; The Simonyi Lecture; Conferences. Notes Full Name. Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. 1 T op ological Manifolds. Further Calculus I. MA8351 DM Notes. Find lecture notes for each section by accessing the chapter links below or using the navigation bar to the left. of Mathematics University of Washington Seattle CONTENTS 1. Department of Mathematics - The University of Manchester Math 103 Lecture 1 notes Types of Problems: 1. Notes on Hellenistic Astronomers and the origins of trigonometry. Shneidman Department of Physics, New Jersey Institute of Technology (Dated: March18,2012). A is an infinite list of numbers written in a defisequence nite order: #ß %ß )ß "'ß$#ß á The numbers in the list are called the of the sequterms ence. Information about the mathematics course, including options, general descriptions of the lecture courses and detailed syllabuses. Introduction. Very useful! Slides from lectures on LaTeX. You see, what gets trans-mitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. Lecture notes: Lectures on Real Analysis, Bonn 2010/ UCLA 2012 , Bonn/UCLA lectures, HT along 1 variable VF, Lecture at the Eli Stein 80 conference 2011 , Powerpoint , Colloquium at Muenster, Amsterdam, Bonn 2011 (3 MB) , Powerpoint , Lectures at Sevilla/Kiel 2010 , Powerpoint , Lectures at Park City 2003 (joint work with T. gz, FR) Lecture Notes on Representation theory by B. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. Undergraduate maths lecture notes (Uni of Cambridge) Here are the lecture notes corresponding to the undergraduate maths degree that I took at the University of Cambridge from 2014-17. Various lecture notes that I've written: Quantum Theory (Part A (2nd year) course in the Oxford Mathematics degree) Lecture notes; Dynamics (Prelims (1st year) course) Lecture notes; Classical Mechanics (Part B (3rd year) course) Lecture notes; Problem sheet 1; Problem sheet 2; Problem sheet 3; Problem sheet 4; Revision sheet. Coding Theory Lecture Notes Nathan Kaplan and members of the tutorial September 7, 2011 These are the notes for the 2011 Summer Tutorial on Coding Theory. Momentum and Its Conservation. Lecture Notes MM805 2018-1. LNIM - Lecture Notes in Mathematics. This section provides the schedule of lecture topics for the course along with lecture notes taken by a student in the class. 140A Lecture Notes Follow. Lecture 1 Systems of algebraic equations The main objects of study in algebraic geometry are systems of algebraic equa-tions and their sets of solutions. Download File PDF Mathematics Of Machine Learning Lecture Notes Mathematics Of Machine Learning Lecture Notes Getting the books mathematics of machine learning lecture notes now is not type of challenging means. in the midst of them is this mathematics of machine learning lecture notes that can be your partner. in Mathematics is mostly of two academic years but it may vary from institute to institute. These are extended lecture notes for a course on transformation groups which I gave at the Mathematical Institute at G~ttingen during the summer term 1978. Complex numbers The equation x2 + 1 = 0 has no solutions, because for any real number xthe square x 2is nonnegative, and so x + 1 can never be less than 1. math 2 notes, Per SBE Rule, students must achieve four high school level units of math in order to graduate with a high school diploma, including Algebra I, Algebra II, and Geometry (or the equivalent courses, Integrated Math I, II, and III) and one additional mathematics course beyond Algebra I. Nikshych: Morita duality for fusion categories and the geometry of modular categories (Lecture 1, Lecture 2). My original intent was to describe the sequence of developments which began in the 1980’s and has led to a uniﬁed and automated approach to ﬁnding partition. Consider the expression $$2^3$$, where $$2$$ is called the base and $$3$$ is called the exponent. Sc Computer Science Lecture Notes Click here to Download: M. Roughly sp eaking, these are ob jects whic h lo cally resem ble a Euclidean space. Besides the textbook, other introductions to Fourier series (deeper but still elementary) are Chapter 8 of Courant-John [5] and Chapter 10 of Mardsen [6]. These lecture notes are based on material from the following books: H. 1 MB) Ses #1-7 complete (PDF - 5. Here is a list of lecture notes and projects used mainly for the course Math 226: Computational PDEs in UC Irvine. Milne (since 1996) Near the end of the lecture, the. Monday, February 1 (pdf of Notes pages 0-8) Includes Section 1. Lecture Notes MATHEMATICAL ECONOMICS A. Hello, I am working through these lecture notes and love them. Stein and R. The text will be edited further during Spring 2012. PROBABILITY THEORY 1 LECTURE NOTES JOHN PIKE These lecture notes were written for MATH 6710 at Cornell University in the allF semester of 2013. They are an ongoing project and are often updated. 46: log likelihood = -367. Lecture Notes in Mathematics listed as LNIM. Homework Help in Basic Math and Pre-Algebra from CliffsNotes! Need help with your Basic Math and Pre-Algebra homework and tests? Literature Notes Test Prep Study. They are aimed at the General Public, schools and anyone who just wants to come along and hear a bit more about what maths is really about. \$ It is the informality that often allows writers of lecture notes or expository articles to mention some "trivial fact" that every textbook leaves out. Lecture notes, etc. 1233: Stability Problems for Stochastic Models. Math 407 Class Lectures. Dold, Heidelberg and B. You see, what gets trans-mitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. There, I ex­plained my work­flow of tak­ing lec­ture notes in LaTeX using Vim and how I draw fig­ures in Inkscape. , Canada, in June of 2000, under the auspices of the Paciﬁc Institute for the Mathematical Sciences. Mathematics site of J. Lecture_Notes (original). Lecture 7 , prt, iClk. Please let us know if you agree to functional, advertising and performance cookies. There is no excerpt because this is a protected post. Additional. Circular Motion and Satellite Motion. It was established in 1964 and was edited by A. Lecture notes for Mathematical Physics Joseph A. This series aims to report newdevelopments in applied and computational mechanics - quickly, informally andat a high level. These lecture notes were written for the course 18. PIMS lecture notes are now available from our new multimedia site http. 11-09-00: Chinese. Eckmann 752 Michael Barr *-Autonomous Categories With an Appendix by Po-Hsiang Chu Springer-Verlag. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. The original publication is available at www. Mathematics for economists is a course webpage produced by Dieter Balkenborg of the University of Exeter, the 2008 version of the course was taught by Juliette Stephenson. UNIX/LIONS - Old Dominion University. Self-Similarity in Deterministic and Stochastic Dissipative Systems Jack Xin. Nilpotence: Lecture 21 42 6. of pages in this PDF lecture notes and the PDF file can be easily downloaded below. Introduction to Mathematical General Relativity : This series of lecture notes were taken for the topic course on mathematical General Relativity given by. Read reviews from world’s largest community for readers. What follows are my lecture notes for Math 4333: Mathematical Biology, taught at the Hong Kong University of Science and Technology. Start with the topic of the discussion (for study purposes later), fill in the date, class, chapters associated with the notes and teacher’s name. Lectures in Algebraic Combinatorics: Young's Construction, Seminormal Representations, SL(2) Representations, Heaps, Basics on Finite Fields (Lecture Notes in Mathematics) by Adriano M. The Lectures Notes correspond to the ﬂrst part of the course devoted to modelling issues to show how the application of models to describe real. Math Camp Notes Lecture Notes (updated August 23, 2017) Lecture 1 (updated August 8, 2017) Lecture 2 (updated August 8, 2017) Lecture 3 (updated August 8, 2017) Lecture 3 Appendix (updated October 25, 2016) Lecture 4 (updated August 8, 2017) Lecture 5 (updated August 8, 2017). · Textbook: I will very loosely follow Wolff’s “Lecture notes on harmonic analysis” and Stein’s “Singular integrals” but rely primarily on my own notes (see below) · Prerequisite: Math 245AB is highly recommended, as is some exposure to undergraduate Fourier analysis (such as Math 133 or equivalent). It is the science of rigorous reasoning. These example sheets are available in PostScript and Adobe Portable Document Format (pdf). The duration of M. ; so h0(0) = 0 and h00(t) = (pa2eta+ (1 tbp)b2e )(peta+ (1 p)etb) (paeta+ (1 p)betb)2. Notes on first-year calculus 29 May 12 Notes on first-year calculus: TeX source 19 Feb 11 Math 3251 updated 26 Sep 05 Math 3252 updated 26 Sep 05, size 1. Lecture Slides As part of a series of lectures on the Clay problems, I spoke in April, 2001 about the Hodge conjecture. Does there exists any good lecture notes for complex analysis which covers all the topics quickly? Like Milne's notes in Algebraic number theory. pdf Lecture Videos 11-01-00: What kinds of problems are solved in discrete math? 11-02-00: Boolean Algebra and formal logic 11-03-00: More logic: quantifiers and predicates 11-06-00: Sets 11-07-00: Diagonalization, functions and sums review 11-08-00: Basic arithmetic and geometric sums, closed forms. 1 PROBABILITY MATTERS The following simple arithmetic rule is frequently used in this section. Hilary 2021. in the midst of them is this mathematics of machine learning lecture notes that can be your partner. As well as giving a geometric basis for many of the relationships of trigonometry. pdf 10/10/12; Lecture Notes/140A_Notes_Ver4. Included as well are stripped-down versions (eg. At the OCW. Over the past decade, statistics have undergone drastic changes with the. Let T : V !W be linear. Suitable for reports, lecture notes and master's theses. The size of a set S, denoted jSj, is known as its cardinality or order. Ciarlet Notes by S. De nition 3. p groups (Lecture 14, 29/10/2015) 31 4. Several Complex Variables (MN-38), Volume 38: Proceedings of the Mittag-Leffler Institute, 1987-1988. Introduction to Page 5/28. National Centre for Mathematics. Included as well are stripped-down versions (eg. Higher derivatives : 5: Implicit differentiation, inverses : 6: Exponential and log. This note covers following topics of Integral and Differential Calculus: Differential Calculus: rates of change, speed, slope of a graph, minimum and maximum of functions, Derivatives measure instantaneous changes, Integral Calculus: Integrals measure the accumulation of some quantity, the total distance an object has travelled, area under a curve. These lecture notes are based on the following books: Samuel A. Of Lecture Notes Mathematics - II (UMA004) Choose a degree at The University of Manchester's Department of Mathematics, and join one of the UK's largest maths departments. Introduction: Newton's Law(s) In Newtonian physics, a particle of mass mmoves through three-dimensional space according to the law. 1 Basic Concepts D. In each lecture, the concepts, theories and methods are taken as the core. Indefinite Integral 2. We wish to present two proofs of (iv): one based on (iii) and (i) and another. The question is very simple: are there good Algebra online lecture notes for a first year course (one semester, US) satisfying the following constraints. Order Date Type Title Author File Attachment Venue ; 17 : Jun, 2007: AIS : Workshop in Comm. 4 completed notes. If you have any enquiries about this website or the content on it, please contact: [email protected] Slides from original lectures: Lecture 1, Lecture 2, Lecture 3, Lecture 4. This series reports on new developments in all areas of mathematics and their applications - quickly, informally and at a high level. 76 pages, 35 figures: Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th). The estimation of parameters can be carried out for this model as follows > z = arima(rrbonds,order=c(1,1,0)) > z Call: arima(x = rrbonds, order = c(1, 1, 0)) Coefficients: ar1 0. 0 MB, December 2005) This is the final version of the notes. This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. Several Complex Variables (MN-38), Volume 38: Proceedings of the Mittag-Leffler Institute, 1987-1988. The material in the current presentation is still meant to be a set of lecture notes, not a text book. Lecture Notes. 7 to construct a power series solution of Gauss’ equation. 1 Set Theory De nition 1 (Set). Date: 1st Jan 2021. We have numbered the videos for quick reference so it's reasonably obvious that each subsequent video. the Pythagorean theorem (Lecture 2), proof by contradiction (Lecture 16), limits (Lecture 18) and proof by induction (Lecture 23). van Wieringen1,2 1 Department of Epidemiologyand Data Science, Amsterdam Public Health research institute, Amsterdam UMC, location VUmc P. The second edition of "Introduction to The Mathematics of Medical Imaging" is now available from SIAM; The webpage for Math 584, 2006. Mathematics is an ancient science and, therefore, it is little wonder that these notes may remind the reader of the other text-books which have already been written and published. The series is a joint effort of the AMS and the Center for Pure and Applied Mathematics at the University of California Berkley (UCB CPAM) (ISSN 1092-9371). Class Notes. The formal name for this class is \Honors Real and Complex Analysis" but it generally goes by simply \Math 55b". The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. Math 155, Lecture Notes- Bonds Name_____ Section 10. ANN ARBOR Chapters 1-3 INTRODUCTION TO PHYSICS. 1 About these notes This is a working set of lecture notes for the Part A Electromagnetism course, which is part of the mathematics syllabus at the University of Oxford. Contents 1 Linear Algebra 7. Indefinite Integral What you need to know:. IB Math has six core topics that both SL and HL students study (for different amounts of time): Topic 1: Algebra; Topic 2: Functions and Equations. While they have been entirely rewritten, the scribe notes served as a crucial motivation to keep writing. This web site is in its final form as of January 21, 1999; the intention is to leave it in place indefinitely. Zl amal: On the nite element method. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. Harmonic functions Updates: 09/27: Margins reduced. Discrete Mathematics Lecture Notes Incomplete Preliminary Version Instructor: L aszl o Babai Last revision: June 22, 2003 Last update: October 24, 2003. Lecture 7 , prt, iClk. Chapter 1 - Introduction to Statistics. Proofs 38 Chapter 6. Here is a list of lecture notes and projects used mainly for the course Math 226: Computational PDEs in UC Irvine. It was established in 1964 and was edited by A. There are links to the corresponding Leeds University Library [email protected] page, in which there are subject notes, videos and examples. ) Lecture 2: Stability and Error Estimates (Stability and error estimates for finite difference schemes for Poisson's equation using the discrete maximum principle. Course Notes and Supplementary Material (PDF format). Collection of Lecture Notes on Mathematics and Physics from University of Cambridge If you're studying mathematics or physics, this link contains a great collection of lecture notes covering almost every topic you'll learn in university, including at the graduate level. A more recent version may be available at ocw. notation name O(1) constant O(log(n)) logarithmic O((log(n))c) polylogarithmic. Dold, Heidelberg and B. Eckmann 752 Michael Barr *-Autonomous Categories With an Appendix by Po-Hsiang Chu Springer-Verlag. Trigonometric limits. Mathematics as a subject is vast and with these online tutorials, we have tried to segregate some major topics into distinct lectures. Lecture Notes for Abstract Algebra I James S. UCI Math 4: Math for Economists (Summer 2013)Lec 01. I am currently referring Tao's lecture notes on complex analysis, but at many points he has referred to Wikepedia so everything is not covered there. 4 completed notes. Printing and bringing a copy of the notes to class will allow you to spend less time trying to write down all of the information and more time understanding the material/problems. Home; LIVE Classes; Our Tutors; Video Lectures. List the two distinct square roots of the number 9. in the midst of them is this mathematics of machine learning lecture notes that can be your partner. The material includes lecture slides, class exercises and solutions, homework tasks, and exam papers, usually made available as PDF files. Mathematics Lecture Series--Waves and Imaging in Random Media. for: Math 259 (Spring 1998): Introduction to Analytic Number Theory Math 155 (Fall 1998): [Combinatorial] Designs and Groups Math 55a (Fall 1999), Math 55b (Spring 1999-2000): Honors Advanced Calculus and Linear Algebra Math 250 (2001-2): Higher Algebra. Tom Nevins and I organized a Special Session on Algebraic Geometry, Representation Theory and Topological Field Theories at the March 2009 UIUC regional meeting of the AMS. Hello Class - There will be no class meeting at the Eagle River Campus on Tuesday, July 18, 2017. l(c) = 1 2 h c+ p c2+ 4 i : 62. Jntuk Materials provides a large collection of lecture notes for Btech Students. The material includes lecture slides, class exercises and solutions, homework tasks, and exam papers, usually made available as PDF files. 14th Oxford-Berlin Young Researchers Meeting on Applied Stochastic Analysis; Past events; Summer. LaTeX Symbols. If this were a proper mathematics course, we would only have 'fundamentals'. Download File PDF Mathematics Of Machine Learning Lecture Notes Mathematics Of Machine Learning Lecture Notes Getting the books mathematics of machine learning lecture notes now is not type of challenging means. Inverse function 2. These lecture notes are from a graduate-level statistics course I taught at the University of California, Berkeley in 2008, 2011, and 2015. Unconstrained Minimization 33 4. AS Level Math Notes & Worksheets. 1 Basic Skills This document contains notes on basic mathematics. Lecture notes Lenya Ryzhik March 1, 2018 Abstract These notes are a compilation of separate original notes by Jim Nolen and Pierre Cardaliaguet, with some very small extra background material, all errors are mine. The Lectures Notes correspond to the ﬂrst part of the course devoted to modelling issues to show how the application of models to describe real. Nevertheless, I hope that this resource would be very helpful for mathematics and physics students, especially those who are interested in Theoretical Physics, or/ and Pure Mathematics. Numerical Computation of Eigenvalues. Next, include the year the notes were taken in parentheses before writing the title of the presentation in italics. Suitable for reports, lecture notes and master's theses. Lecture Notes: The files posted below are lecture notes from some previous courses that I've taught. Collection of Lecture Notes on Mathematics and Physics from University of Cambridge If you're studying mathematics or physics, this link contains a great collection of lecture notes covering almost every topic you'll learn in university, including at the graduate level. LNIM - Lecture Notes in Mathematics. This series reports on new developments in all areas of mathematics and their applications - quickly, informally and at a high level. MATH-ECON Courses: OPMT 7701 (BCIT) ECON 331 (SFU) ECON 431 (SFU) Home : Fundamental Methods of. Other students are also welcome to enroll, but must have the necessary mathematical skills. ANN ARBOR Chapters 1-3 INTRODUCTION TO PHYSICS. Activity: Lecture. We have numbered the videos for quick reference so it's reasonably obvious that each subsequent video. Eigenvalue problems Eigenvalue problems occur in many areas of science and engineering, such as structural analysis Eigenvalues are also important in analyzing numerical methods Theory and algorithms apply to complex matrices as well as real matrices With complex matrices, we use conjugate transpose, AH, instead of usual. connection with a fundamental mathematical result called the Binomial Theorem; you may also recall the related “Pascal’s Triangle”). Whenever I have one of. has very important mathematical properties, but it is very difficult to provide a substantive definition. MA 161 (Spring 2020), lecture notes are here due to the shift to online classes, the videos for lessons 22-35 are here MA 162 (Fall 2019), lecture notes are here MA 303 (Summer 2019), lecture notes are here (Summer 2017 (old 303) notes are here) MA 161 (Spring 2019), lecture notes are here MA 265 (Summer 2018), lecture notes are here. Math 244 Lecture Notes Chapter 18: Confidence Intervals for 1-Proportion Overview: Today, we will look at how information about samples (statistics) can be used to make predictions about information about larger populations (parameters). They were typed up by a student in my year during the lectures, and to be honest most of the time I found it easier to learn from these than the actual lectures. Lecture notes and articles are where one generally picks up on historical context, overarching themes (the "birds eye view"), and neat interrelations between subjects. This series aims to report newdevelopments in applied and computational mechanics - quickly, informally andat a high level. If you find any typos or inaccuracies, or if you have any suggestions on how to improve the notes (aesthetically or otherwise), send me an email at ude. Printing and bringing a copy of the notes to class will allow you to spend less time trying to write down all of the information and more time understanding the material/problems. pdf: Lecture 8: Data Handling and Program Control Flow Instructions: LECT08. 00 (少于10人评价). Lecture notes on minimal surfaces: This series of lecture notes were taken for the topic course on minimal surfaces given by Professor Rick Schoen in the Winter quarter of 2012 at Stanford. IB Math has six core topics that both SL and HL students study (for different amounts of time): Topic 1: Algebra; Topic 2: Functions and Equations. edu/courses/math_4_math_for_economists. 09/26: Removed all mentions of the word "domain". The notes focus on the construction of numerical algorithms for ODEs and the mathematical analysis of their behaviour, cov-ering the material taught in the M. These lecture notes are from a graduate-level statistics course I taught at the University of California, Berkeley in 2008, 2011, and 2015. Its format is book, but I have some difficulties with it. Each of the books contains 15 chapters, called lectures — I may only guess why. 1 About these notes This is a working set of lecture notes for the Part A Electromagnetism course, which is part of the mathematics syllabus at the University of Oxford. A program in Quantum Field Theory for mathematicians was held at the Institute for Advanced study during the academic year 1996-97. Included are detailed discussions of Limits (Properties, Computing, One-sided, Limits at Infinity, Continuity), Derivatives (Basic Formulas, Product/Quotient/Chain Rules L'Hospitals Rule, Increasing/Decreasing/Concave Up/Concave Down, Related Rates, Optimization) and basic Integrals (Basic Formulas. List the two distinct square roots of the number 9. There are usually English, science, and math sections. These notes are intended to be a summary of the main ideas in course MATH 214-2: Integral Calculus. the Pythagorean theorem (Lecture 2), proof by contradiction (Lecture 16), limits (Lecture 18) and proof by induction (Lecture 23). Lecture Notes 1. Math Homework Assignment Lecture Notes. Sign In; Register; Scientific. definition-only; script-generated and doesn't necessarily make sense), example sheets, and the source code. Rockafellar Dept. 1 We begin by describing a rather general framework for the derivation of PDEs. 1 Basic Skills This document contains notes on basic mathematics. 2 to page 153 Definition: Descriptively realistic. A rigorous introduction up through Riemann Integration, including an overview of the Fundamental Existence and Uniqueness Theorem for Ordinary Differential. 2 completed notes. 9--55 Serge Lang Equidimensional higher dimensional theory. 9GB1 Project Preparation LaTeX material. Nature of Mathematics Great ideas and gems of mathematics. Ans: 1 4 (49 log 7 − 75 2 log 5 − 27 log 3 + 6). Numerical Solution of Scalar Equations. Math 1140 Fall 2011. Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. 4 Thelanguageoflogic. A program in Quantum Field Theory for mathematicians was held at the Institute for Advanced study during the academic year 1996-97. Asymptotes. com-2021-01-27-05-58-34 Subject: Business Mathematics Lecture Notes Keywords: business,mathematics,lecture,notes Created Date: 1/27/2021 5:58:34 AM. CONTENTS iii 2. Written on December 29, 2008 Tweet. This course is the basic course in mathematical logic, presenting Gödel’s completeness theorem and related subjects. Hello, I am working through these lecture notes and love them. tex in the di­rec­to­ry complex- analysis and mas­ter. MATH 1012 Lecture Notes 2 Topics covered in lecture 02: 1. LECTURE NOTES 2007 R. With some exceptions, the exposition follows the textbook Complex Analysis by E. gz, FR) Lecture Notes on Representation theory by B. Transcribed by Julien Edward Clancy (edited by Asad Lodhia, Elchanan Mossel and Matthew Brennan) Last lecture we saw the most basic theorem about neural network approximation: that for most activation functions, including any $$\sigma \colon \mathbb{R} \to \mathbb{R}$$ such that $$\sigma(x) \to 0$$ as $$x \to -\infty$$ and $$\sigma(x) \to 1$$ as $$x \to \infty$$, and also including.