Courses tagged with "Structural engineering" (124)

Statistics 2 at Berkeley is an introductory class taken by about 1,000 students each year. Stat2.3x is the last in a sequence of three courses that make up Stat2x, the online equivalent of Berkeley's Stat 2. The focus of Stat2.3x is on statistical inference: how to make valid conclusions based on data from random samples. At the heart of the main problem addressed by the course will be a population (which you can imagine for now as a set of people) connected with which there is a numerical quantity of interest (which you can imagine for now as the average number of MOOCs the people have taken). If you could talk to each member of the population, you could calculate that number exactly. But what if the population is so large that your resources will not stretch to interviewing every member? What if you can only reach a subset of the population?

Stat 2.3x will discuss good ways to select the subset (yes, at random); how to estimate the numerical quantity of interest, based on what you see in your sample; and ways to test hypotheses about numerical or probabilistic aspects of the problem.

The methods that will be covered are among the most commonly used of all statistical techniques. If you have ever read an article that claimed, "The margin of error in such surveys is about three percentage points," or, "Researchers at the University of California at Berkeley have discovered a highly significant link between ...," then you should expect that by the end of Stat 2.3x you will have a pretty good idea of what that means. Examples will range all the way from a little girl's school science project (seriously – she did a great job and her results were published in a major journal) to rulings by the U.S. Supreme Court.

The fundamental approach of the series was provided in the description of Stat2.1x and appears here again: There will be no mindless memorization of formulas and methods. Throughout the course, the emphasis will be on understanding the reasoning behind the calculations, the assumptions under which they are valid, and the correct interpretation of results.

Statistics 2 at Berkeley is an introductory class taken by about 1000 students each year. Stat2.2x is the second of three five-week courses that make up Stat2x, the online equivalent of Berkeley's Stat 2.

The focus of Stat2.2x is on probability theory: exactly what is a random sample, and how does randomness work? If you buy 10 lottery tickets instead of 1, does your chance of winning go up by a factor of 10? What is the law of averages? How can polls make accurate predictions based on data from small fractions of the population? What should you expect to happen "just by chance"? These are some of the questions we will address in the course.

We will start with exact calculations of chances when the experiments are small enough that exact calculations are feasible and interesting. Then we will step back from all the details and try to identify features of large random samples that will help us approximate probabilities that are hard to compute exactly. We will study sums and averages of large random samples, discuss the factors that affect their accuracy, and use the normal approximation for their probability distributions.

Be warned: by the end of Stat2.2x you will not want to gamble. Ever. (Unless you're really good at counting cards, in which case you could try blackjack, but perhaps after taking all these edX courses you'll find other ways of earning money.)

The fundamental approach of the series was provided in the description of Stat2.1x and appears here again: There will be no mindless memorization of formulas and methods. Throughout the course, the emphasis will be on understanding the reasoning behind the calculations, the assumptions under which they are valid, and the correct interpretation of results.

FAQ

• What is the format of the class?
  • Instruction will be consist of brief lectures and exercises to check comprehension. Grades (Pass or Not Pass) will be decided based on a combination of scores on short assignments, quizzes, and a final exam.
• How much does it cost to take the course?
  • Nothing! The course is free.
• Will the text of the lectures be available?
  • Yes. All of our lectures will have transcripts synced to the videos.
• Do I need to watch the lectures live?
  • No. You can watch the lectures at your leisure.
• Will certificates be awarded?
  • Yes. Online learners who achieve a passing grade in a course can earn a certificate of achievement. These certificates will indicate you have successfully completed the course, but will not include a specific grade. Certificates will be issued by edX under the name of BerkeleyX, designating the institution from which the course originated.
• Can I contact the Instructor or Teaching Assistants?
  • Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.
• Do I need any other materials to take the course?
  • If you have any questions about edX generally, please see the edX FAQ.

People sometimes think that math is just about number crunching. However, that’s not always the case. Patterns and letters (called variables) are used in math to help represent real-life situations. In addition to learning about variables, parts of this course will help you see a side of math you might not have even realized is out there. This course includes six units. Topics covered include multiplication and division of fractions, ratio reasoning, unit rates, expressions, equations, area, surface area, volume, and statistics. As you work through the six units, you will notice that some of the material builds on your prior knowledge, while some of the concepts will be new ideas that will serve as building blocks for your future math career. In unit 1, you will build on your current understanding of fractions, multiplication, and division to understand why the procedures for multiplying and dividing fractions make sense. The number system in its basic sense is probably already familiar to you. During…

Numbers are everywhere. When we are shopping we are faced with decimals. In our cooking, we work with fractions. When it comes to the stock market, we can see positives and negatives. In this course, we will we focus on these rational numbers and understanding the operations when working with them. This course includes five units with rational numbers used throughout. In Unit 1, we will build on our skills with integers, decimals, and fractions, with a focus on the properties that are at the heart of adding, subtracting, multiplying, and dividing. These skills are used to help build an understanding of proportional relationships through ratios, rates, and scale drawings, and similar figures in Unit 2. Variables will join the rational numbers in Unit 3 so that real-life mathematical problems can be expressed and solved. Mathematical reasoning will continue to grow in this unit as simple equations and inequalities are used to model different real-life scenarios. Two-dimensional and three-dimensional shapes…

Algebra is incorporated into a lot of daily activities even when you don’t realize you are using it. Whether you are planning a vacation, deciding on a job, shopping, building something, planning a party, monitoring your heartbeat, or dieting, algebra can help you get a job done or make successful decisions. This course includes 10 units that will help you in this endeavor. This course is a continuation of the development of concepts and problem-solving methods learned in pre-algebra courses. Topics in this course include expressions, functions, equations and inequalities, exponentials, quadratics, piecewise and absolute value functions, systems, and statistics. The purpose of this course is to build a strong algebra background that is needed to be successful in the upper level mathematics courses, as well as to gain the logic needed to solve real-world applications. In Unit 1, you will build on your skills with activities that will help with the modeling and graphing in all future units. You will also…

Geometry comes from the Greek roots geo-, meaning Earth, and metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms…

The purpose of this course is to familiarize you with the fundamentals of algebraic expressions, including adding, multiplying, factoring, and simplifying; solving equations and inequalities; performing operations on functions; and performing graphing and basic functional analysis. This course is intended to extend your knowledge beyond the foundational information learned in Algebra I and prepare you for more advanced topics, leading toward trigonometry and calculus. Among the benefits that you will gain from learning the material contained here are adding tools for critical thinking, improving skill sets for use in the sciences, and improving your competitiveness in preparation for college applications. A strong understanding of mathematics is critical toward earning scholarships and gaining admission to many top universities, and the knowledge gained here will help in that regard.

Mathematics comes together in this course. You enter precalculus with an abundant array of experience in mathematics, and this course offers an opportunity to make connections among the big ideas you encountered earlier. It also assists you in developing fluency with the tools used in learning calculus. The focus of this course is the concept of function - it’s with functions that mathematicians and scientists can model the world and make leaps of invention, sending rockets to far planets, determining the future size of populations, and finding the amount of earth to be moved when creating new roads. The unit begins by defining and exploring certain attributes of functions and continues with specific kinds of functions - linear, polynomial, rational, logarithmic, and exponential. In addition to precalculus being important for many fields, the subject is obviously designed to prepare you for calculus, which is the mathematics of things that are changing. Calculus allows us to find areas of strangely curv…

Calculus AB is primarily concerned with developing your understanding of the concepts of calculus and providing you with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are also emphasized. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types, but rather, the course uses the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling to become a cohesive whole. The course is a yearlong high school mathematics course designed to prepare you to write and pass the AP Calculus AB test in May. Passing the test can result in one semester of college credit in mathematics.

Welcome to the amazing world of statistics! You might be thinking that the topic is just about a bunch of charts, graphs, and odd-looking formulas, but in fact, it is a fascinating and challenging field of study. In this course, we will indeed study those charts and graphs, and yes, that array of complex formulas. But beyond those tools, we will find an entire new way of thinking, a new way of approaching and understanding the world around us. We will learn why taking aspirin helps lower the risk and severity of a heart attack; how researchers have determined that the more friends you have on a social networking site, the more likely you are to have fewer friends in real life; and how political pollsters almost always know the outcome of an election even before the polls open. The course is divided into 10 units of study. The first two units are devoted to simple statistical calculations and graphical representations of data. Most of this material will be familiar to you from previous math or science course…

Is my program correct?  Will it give the right output for all possible permitted inputs?  Computers are now essential in everyday life.  Incorrect programs lead to frustration in the best case and disaster in the worst. Thus, knowing how to construct correct programs is a skill that all who program computers must strive to master. 

In this computer science course, we will presents "goal oriented programming" the way Edsger Dijkstra, one of the most influential computer scientists, intended. You will learn how to derive programs hand-in-hand with their proofs of correctness. The course presents a methodology that illustrates goal-oriented programming, starting with the formalization of what is to be computed, and then growing the program hand-in-hand with its proof of correctness. The methodology demonstrates that, for a broad class of matrix operations, the development, implementation, and establishment of correctness of a program can be made systematic.

Since this technique focuses on program specifications, it often leads to clearer, correct programs in less time. The approach rapidly yields a family of algorithms from which you can then pick the algorithm that has desirable properties, such as attaining better performance on a given architecture. 

The audience of this MOOC extends beyond students and scholars interested in the domains of linear algebra algorithms and scientific computing. This course shows how to make the formal derivation of algorithms practical and will leave you pondering how our results might extend to other domains.

As a result of support from MathWorks, learners will be granted access to MATLAB for the duration of the course.

This introductory computer science course in machine learning will cover basic theory, algorithms, and applications. Machine learning is a key technology in Big Data, and in many financial, medical, commercial, and scientific applications. It enables computational systems to automatically learn how to perform a desired task based on information extracted from the data. Machine learning has become one of the hottest fields of study today and the demand for jobs is only expected to increase. Gaining skills in this field will get you one step closer to becoming a data scientist or quantitative analyst.

This course balances theory and practice, and covers the mathematical as well as the heuristic aspects. The lectures follow each other in a story-like fashion:

• What is learning?
• Can a machine learn?
• How to do it?
• How to do it well?
• Take-home lessons.

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

• It’s visual.
• It connects hand calculations, mathematical abstractions, and computer programming.
• It illustrates the development of mathematical theory. 
• It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

We invite you to LAFF with us!

Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

• It’s visual.
• It connects hand calculations, mathematical abstractions, and computer programming.
• It illustrates the development of mathematical theory.
• It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

This summer version of the course will be released at an accelerated pace. Each of the three releases will consist of four ”Weeks” plus an exam . There will be suggested due dates, but only the end of the course is a true deadline.

We invite you to LAFF with us!

FAQs

What is the estimated effort for the course? 

About 8 hrs/week.

How much does it cost to take the course?

You can choose! Auditing the course is free.  If you want to challenge yourself by earning a Verified Certificate of Achievement, the contributions start at $50.

Will the text for the videos be available?

Yes. All of our videos will have transcripts synced to the videos.

Are notes available for download?

PDF versions of our notes will be available for free download from the edX platform during the course.  Compiled notes are currently available at www.ulaff.net.

Do I need to watch the videos live?

No. You watch the videos at your leisure.

Can I contact the Instructor or Teaching Assistants?

Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.

Is this course related to a campus course of The University of Texas at Austin?

Yes. This course corresponds to the Division of Statistics and Scientific Computing titled “SDS329C: Practical Linear Algebra”, one option for satisfying the linear algebra requirement for the undergraduate degree in computer science.

Is there a certificate available for completion of this course?

Online learners who successfully complete LAFF can obtain an edX certificate. This certificate indicates that you have successfully completed the course, but does not include a grade.

Must I work every problem correctly to receive the certificate?

No, you are neither required nor expected to complete every problem.

What textbook do I need for the course?

There is no textbook. PDF versions of our notes will be available for free download from the edX platform during the course. Compiled notes are currently available at www.ulaff.net.

What are the principles by which assignment due dates are established?

There is a window of 19 days between the material release and the due date for the homework of that week. While we encourage you to complete a week’s work before the launch of the next week, we realize that life sometimes gets in the way so we have established a flexible cushion. Please don’t procrastinate. The course closes 25 May 2015. This is to give you nineteen days from the release of the final to complete the course.

Are there any special system requirements?

You may need at least 768MB of RAM memory and 2-4GB of free hard drive space. You should be able to successfully access the course using Chrome and Firefox.

Phenomena as diverse as the motion of the planets, the spread of a disease, and the oscillations of a suspension bridge are governed by differential equations. This course is an introduction to the mathematical theory of ordinary differential equations and follows a modern dynamical systems approach. In particular, equations are analyzed using qualitative, numerical, and if possible, symbolic techniques.

MATH226 is essentially the edX equivalent of MA226; a one-semester course in ordinary differential equations taken by more than 500 students per year at Boston University. It is divided into three parts. MATH226.2x is the second part.

For additional information on obtaining credit through the ACE Alternative Credit Project, please visit here.

Precalculus I is designed to prepare you for Precalculus II, Calculus, Physics, and higher math and science courses. In this course, the main focus is on five types of functions: linear, polynomial, rational, exponential, and logarithmic. In accompaniment with these functions, you will learn how to solve equations and inequalities, graph, find domains and ranges, combine functions, and solve a multitude of real-world applications. In this course, you will not only be learning new algebraic techniques that are necessary for other math and science courses, but you will be learning to become a critical thinker. You will be able to determine what is the best approach to take such as numerical, graphical, or algebraic to solve a problem given particular information. Then you will investigate and solve the problem, interpret the answer, and determine if it is reasonable. A few examples of applications in this course are determining compound interest, growth of bacteria, decay of a radioactive substance, and the…

Precalculus II continues the in-depth study of functions addressed in Precalculus I by adding the trigonometric functions to your function toolkit. In this course, you will cover families of trigonometric functions, as well as their inverses, properties, graphs, and applications. Additionally, you will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations. You might be curious how the study of trigonometry, or “trig,” as it is more often referred to, came about and why it is important to your studies still. Trigonometry, from the Greek for “triangle measure,” studies the relationships between the angles of a triangle and its sides and defines the trigonometric functions used to describe those relationships. Trigonometric functions are particularly useful when describing cyclical phenomena and have applications in numerous fields, including astronomy, navigation, music theory, physics, chemistry…

Calculus can be thought of as the mathematics of CHANGE. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT. Solving an algebra problem, like y = 2x + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt, where t is elapsed time and X0 is the initial deposit. With compound interest, things get complicated for algebra, as the rate R is itself a function of time with Y = X0 + R(t)t. Now we have a rate of change which itself is changing. Calculus came to the rescue, as Isaac Newton introduced the world to mathematics specifically designed to handle those things that change. Calculus is among the most important and useful developments of human thought. Even though it is over…

This course is the second installment of Single-Variable Calculus.  In Part I (MA101) [1], we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions.  In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned. Additional integration techniques, in particular, are a major part of the course.  In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution.  In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms.  Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you’d like. Integration allows us to calculat…

Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions.  You may find that these courses share many of the same basic concepts, and that Multivariable Calculus will simply extend your knowledge of functions to functions of several variables.  The transition from single variable relationships to many variable relationships is not as simple as it may seem; you will find that multi-variable functions, in some cases, will yield counter-intuitive results. The structure of this course very much resembles the structure of Single-Variable Calculus I and II.  We will begin by taking a fresh look at limits and continuity.  With functions of many variables, you can approach a limit from many different directions.  We will then move on to derivatives and the process by which we generalize them to higher dimensions.  Finally, we will look at multiple integrals, or integration over regions of space as opposed to intervals. The goal of Mu…