Mathematics: Math Models & Their Analysis

See Schedule of Courses for specific titles.

Prereqs: MATH 2248; MATH 2522 or MATH 2524; Open to Degree and PACE students Special Topics courses cannot carry CC designations

https://tlakoba.w3.uvm.edu/AppliedUGMath/

<p>The website listed above refers to the edition of this course offered in Spring 2021. While it will be edited in Spring 2026, the main material, such as lecture notes, homework assignments, and the information about midterm project papers, will remain (mostly) the same.</p> <p> In this course, several models of classical and modern science are considered starting, as much as possible, from the first principles. Examples include: Formation of rainbows, Motion on a roller-coaster, Input-output models in economics, Nonlinear pendula (including an inverted pendulum), Smoothing of noisy experimental data, and The black body radiation. The emphasis in describing each model is made on presenting mathematical techniques which are: (i) commonly used by applied mathematicians, physicists, and engineers, and (ii) are covered in the undergraduate courses on Calculus and Linear Algebra. Examples of such techniques are: linearization, Taylor series, and eigenvector expansions. Thus, one of the goals of this course is to show the students some real-world applications of these fundamental techniques.</p> <p>The other major goal of this course is to coach students on giving oral presentations. To this end, the course includes (instead of exams) two projects: a midterm and a final, where the students are to read a contemporary research paper (with some mathematical content) and give a presentation about it to the class. Before each presentation, every student is required to practice his/her talk in front of the instructor, and the instructor gives the feedback and advice on how to improve the talk. The feedback is also given after each presentation. </p> <p>There is <b>no</b> required textbook for this course. You will need to study the notes posted on the course website listed above. </p>

<br><br> <strong>Homework </strong> will be assigned approximately once a week, at the end of each section. <br><br> <strong>Tests:</strong> There will be <b>no</b> tests in this course. Instead, you will do two projects (presentations), as described below. <br><br> <strong>Projects: </strong>   There will be two projects, a midterm and a final. <br> <p> The midterm project will be based on an application of Singular Value Decomposition. This will be a class project in that the presentation material will be divided among the students, and each student will present his or her part. You will be graded on <b><em>both the content and the style of your presentation</em></b>.<br> For the final project, you will make a presentation to the class about a paper or a section in a book of your own choosing. (This text has to be related to applied mathematics.) Your goal will be to convey the main results of the scientific text and demonstrate that you were able to follow its calculations.</p> <p><b><u>Practicing your presentations</u></b>:   As an important objective of this course is to learn how to give presentations, you will be <b>required</b> to rehearse each of your two talks in front of the instructor. <br><br>

<br>The following policy is <u>approximate</u>. Refer to the syllabus distributed at the beginning of the semester for the actual policy. <br> <li> Homework = 40 %;</li> <li> Midterm project = 25 %;</li> <li> Final project = 35 %.</li>