Duke math 361

As a general rule, un-mathematics-manlike behaviors will be frowned upon. Calculators will be prohibited in all the rounds. And all numerical answers should be reduced to the simplest form. The Power Round is a multi-part proof problem. All the problems will be related in one topic. The team members will work together on these problems. Answers should be given in the form of mathematical proofs, unless otherwise stated.

All the necessary work to justify an answer and all the necessary steps of a proof must be shown clearly to obtain full credit. Partial credit may be awarded for answers that are incomplete but making a progress toward the solution. On each sheet you turn in, indicate the problem number in the upper left-hand corner and your team number in the upper right-hand corner. Do not write your team name anywhere on your answers. Do not put answers to differently numbered problems on the same sheet.

The Team Round consists of ten questions with numerical answers. In this round, the team members will also work together and turn in a single answer sheet. The answer should be accurate and simplified, following the Numerical Answering Guideline.

Leaving a question blank does not yield extra points, nor do wrong answers receive any penalties. The round will be consist of 10 questions split into 5 pairs. Participants receive one pair at a time, and have 10 minutes to solve the two problems given. Each question will be worth 1 point with 10 points total. The correct answer to all 10 problems will be posted at the end of the round.

The answer, and only the answer should be written on the answer sheet provided by the proctor. The answer should be reduced to the lowest possible form, fractions and radicals needs to be reduced.

The individual score is the sum of the scores of all 8 questions. In case of ties, the tie will be broken during the Lightning round. Each team will be broken down into groups of 3. Each of the 3 people will receive a different problem. When the first person solves his or her problem, he writes the answer on a small piece of paper and passes it to the right or the left depending on which side of the auditorium you are on.Newtonian mechanics at the intermediate level, Lagrangian mechanics, linear oscillations, chaos, dynamics of continuous media, motion in noninertial reference frames.

Prerequisite: MATH or equivalent may be taken concurrently. One course.

duke math 361

Newtonian dynamics, conservation laws, systems of many particles, ocsillatory motion, damped and driven oscillators, resonance, impulse response, coupled oscillators, Hamilton principle, Lagrangian mechanics, Hamilton's and Lagrange's equations of motion, Noether's theorem and conservation laws, central force problems, Kepler's planetary motion, scattering by central forces, non-inertial reference frames, dynamics of rigid bodies, inertia tensor, Euler angles and equations, motion of a symmetric top, dynamics of continuous media, identical coupled oscillators and continuum limit, wave equation and boundary conditions, wave packets, phase velocity, group velocity, dispersion, non-linear systems.

In early attempts to understand the fundamental pieces of nature and the rules that govern how these pieces interact, scientists explored two paths in parallel, that the basic objects in the universe were localized particles or rigid groups of such particles or that the basic objects were spatially extended entities similar to waves.

PHYSICS discusses the first of these points of view, how to describe nature in terms of the motion of particles or of rigid bodies. In contrast, PHYSICSthe core course on electrodynamics, discusses how to describe nature in terms of the dynamics of spatially extended fields, such as electric and magnetic fields.

Experiments later showed that the fundamental particles in nature like a photon or electron act neither like particles nor like waves but like something else, which is discussed first in PHYSICS and in more depth in the introductory quantum physics course, PHYSICS The undergraduate mechanics course introduces new more sophisticated ways associated with the names of Hamilton and Lagrange to describe the motion of particles and rigid objects.

These new ways have multiple advantages over Newton's three laws of motion. This turns out to greatly simplify many mechanics problems, which become easier to solve. The Lagrange formulation especially makes clear something that is difficult to deduce from Newton's laws, which is a deep connection between symmetry and the evolution equations for a system of particles.

This connection later played a central role in the development of theories of subatomic particles. It turns out that quantum mechanics has remarkable mathematical similarities to classical mechanics which is an important reason to take before and can also be expressed in a Lagrangian form.

It is then possible to guess what are the laws of interaction of subatomic particles such as the strong interaction by guessing what symmetries might govern their behavior. It is in PHYSICSvia the Lagrange and Hamilton formulations of mechanics, that you get to understand particularly clearly why there are additive conservation laws for energy, momentum, and angular momentum but generally not for other quantities.

These conservation laws turn out to reflect fundamental symmetries of space and time. For example, energy conservation is associated with the observation that when an experiment is carried out does not affect the results of the experiment, this is the symmetry of time translation invariance.

Momentum conservation is associated with the observation that where an experiment is carried does not affect the results and is associated with the symmetry of space translation invariance, and similarly for angular momentum.

duke math 361

A puzzle for you to think about: are all conservation laws related to some symmetry? If so, what is the symmetry that corresponds to conservation of charge? Skip to main content Intermediate Mechanics PHYSICS Newtonian mechanics at the intermediate level, Lagrangian mechanics, linear oscillations, chaos, dynamics of continuous media, motion in noninertial reference frames.Students can post questions and collaborate to edit responses to these questions. Instructors can also answer questions, endorse student answers, and edit or delete any posted content.

Piazza is designed to simulate real class discussion. It aims to get high quality answers to difficult questions, fast! The name Piazza comes from the Italian word for plaza--a common city square where people can come together to share knowledge and ideas. We strive to recreate that communal atmosphere among students and instructors.

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Sample Course Schedules

Welcome to Piazza! Please enter your school email address Please enter the duke. Email: Confirm Email: Please enter a valid duke.An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries mathematically evaluate the probability of events and quantify the contingent outcomes in order to minimize the impacts of financial losses associated with uncertain undesirable events. The profession has consistently ranked as one of the most desirable in various studies over the years.

The first two exams are:. Previous versions of these exams, with answer keys and solutions, and information about submitting an application for the exams, can be found online at Be An Actuary. The CAS Syllabus of Examinations and the Education Area of the SOA web site contain a description of the education and examination system for the Preliminary Actuarial Examinations, including the material to be covered for each examination, instructions, schedules, and applications.

Students can find links to this information at Be An Actuary. The following is a list of Duke courses that are useful in preparing for a career as an actuary. A directory of approved college courses is available at the VEE requirements home page. You may apply for VEE credit for your coursework after you have passed the first two exams. FAP is an e-Learning course that includes both online and offline activities and exposes you to real-world situations.

For further information or additional advice about careers in the actuarial sciences, please contact Professor Amy Herring of the Department of Statistical Science, Duke math alumnus Emily Reithernow at Allstate, or alumnus Andrew Tignanelli.

Descriptions of these courses can be found on the UNC curriculum website. Under a reciprocal agreement between the two universities, students at Duke may enroll concurrently in these courses offered by UNC. Note, however, that prior approval from the Director of Undergraduate Studies must be sought for such courses to count toward mathematics major or minor credit. Charles W. Dunna Duke graduate and Fellow of the Society of Actuaries, teaches the UNC courses and will be happy to answer questions about them or about actuarial science in general.

Check out their website for more information. Many professions and many graduate and professional school programs regard a strong background in mathematics as highly desirable.

For that reason, students with a primary interest in other disciplines may also want to consider a major or minor in mathematics. For students interested in Engineering or Natural Sciences, the following courses are recommended:.

A student planning to pursue graduate study in mathematics should develop a program of study that provides both variety of experience and a strong background in fundamental areas.Announcements regarding distance learning The syllabus has been updated with changes in the class format and policies. Lecture videos will be recorded and made available on Sakai.

You are asked to watch the videos before class time, and are encouraged to ask questions and discuss the lecture on the Piazza page.

Class time will be devoted to discussion and to working out examples. We will experiment with the format, but the general plan is to a first devote some time to QA on the relevant material, b work out practice problems, and c show demos involving code.

All homework is to be submitted on Sakai. I will not check my mailbox. Access virtual class meetings and office hours through Sakai using Zoom.

duke math 361

To access the meeting, log on to Sakai and click on "Zoom Meetings" on the left, then click "Join" beside the meeting. Feel free to email me to schedule meetings at other times; these will also be conducted using Zoom. Let me know if you have any issues with using it. Exam II has been postponed to April It will likely be structured as a take-home exam.

Mathematical Numerical Analysis

This includes but is not limited to: Not being available at the regular class time e. Description Development of numerical techniques for accurate, efficient solution of problems in science, engineering, and mathematics through the use of computers. Linear systems, nonlinear equations, optimization, interpolation, numerical integration, differential equations, error analysis.

Prerequisites Solid understanding of fundamental concepts from linear algebra is essential, including linearity, solving linear systems, eigenvalues and eigenvectors. A course in multi-variable calculus e. Math is also required. Experience with ordinary differential equations is recommended, but not necessary. Homework Homework will be assigned roughly weekly and will typically be due the following Wednesday. Consult the schedule for due dates. No late homework will be acceptedbarring exceptional circumstances as per Duke policy.

Working and studying in groups is encouraged you will get much more out of doing homework if you discuss it with others! However, you should write your own solutions to each problem in your own words. Solutions should be complete arguments; the process by which you arrive at the solution is far more important than a correct answer. Assertions should be supported by computed data and code when it is needed. Homework pages must be stapled together with clearly readable work.

Solutions should be in the same order as in the list of assigned problems. Computational work Some homework problems will require writing and running code.

The official programming language for this course is Matlab, but you may write your code in Matlab, Python, or Julia. Collaboration is encouraged but the code you submit should be your own, which includes not copy-pasting code from other sources.

Avoid looking up code online because it is difficult to un-see it when writing your own.

duke math 361

Ethics Students are expected to follow the Duke Community Standard.Emily Jorgens '14 helped build a website to match immunocompromised people in Santa Clara County, Calif. Brandon Yan '18 and Brian McSteen '14, medical students at the University of California-San Francisco, are helping lead a donation drive to get nearly 20, face masks into the hands of clinicians.

Have you heard about a fellow Blue Devil going above and beyond for their community during this time? We want to hear from you. Exercise your brain without leaving your home. Read the most recent Forever Learning newsletter for the latest livestreams and recorded webinars by Duke, for Duke.

More than ever, students need the support of the Duke alumni community. Update your profile and contact information on the alumni network so students can find you and message you. If your company has career opportunities for students including short-term projects or remote work, post to the Duke Alumni Job Board. This fund will benefit students in all schools and will help alleviate the unexpected burden of student expenses such as airline tickets, temporary housing, meals, technology for online learning and more.

Follow DukeAlumni on your favorite social networks to stay in-the-know. Join the Blue Crew to become a social media ambassador. Read President Vincent E. Skip to main content. Duke University has adopted new policies for events. Read more about the DAA events that will be impacted. Be Part of the Change Our commitment to standing against systemic racism Read. New to this site? Homepage Find Content Sign in now to:.

Read more about this notable alum. Read More. Supply Chain Brandon Yan '18 and Brian McSteen '14, medical students at the University of California-San Francisco, are helping lead a donation drive to get nearly 20, face masks into the hands of clinicians. Share a Story Have you heard about a fellow Blue Devil going above and beyond for their community during this time? Keep Learning with Duke Exercise your brain without leaving your home.

Help Duke Students More than ever, students need the support of the Duke alumni community. Donate to the Duke Student Assistance Fund This fund will benefit students in all schools and will help alleviate the unexpected burden of student expenses such as airline tickets, temporary housing, meals, technology for online learning and more.

Connect with Duke. Be Social Follow DukeAlumni on your favorite social networks to stay in-the-know.Description Development of numerical techniques for accurate, efficient solution of problems in science, engineering, and mathematics through the use of computers.

Linear systems, nonlinear equations, optimization, numerical integration, differential equations, error analysis. Prerequisites solid understanding of fundamental concepts from linear algebra is essential, including linearity, solving linear systems, eigenvalues and eigenvectors. A course in multi-variable calculus e. Math is also required. Experience with ordinary differential equations is recommended, but not necessary.

Homework Homework will be assigned roughly weekly and will typically be due the following Wednesday. Consult the schedule for due dates. No late homework will be acceptedbarring exceptional circumstances as per Duke policy. Working and studying in groups is encouraged you will get much more out of doing homework if you discuss it with others! However, you should write your own solutions to each problem in your own words.

Solutions should be complete arguments; the process by which you arrive at the solution is far more important than a correct answer. Assertions should be supported by computed data and code when it is needed. Homework pages must be stapled together with clearly readable work.

Solutions should be in the same order as in the list of assigned problems. Computational work Some homework problems will require writing and running code.

You may write your code in Matlab or python for python, use the numpy package. Collaboration is encouraged but the code you submit should be your own, which includes not copy-pasting code from other sources.

Intermediate Mechanics

Avoid looking up code online because it is difficult to un-see it when writing your own. Expectations for computational problems are detailed in the Guidelines for computational problems document on Piazza. Ethics Students are expected to follow the Duke Community Standard. If a student is found responsible for academic dishonesty through the Office of Student Conduct, the student will receive a core of zero for that assignment.


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