AMATH 352

Course Topics:

(1) Spectral and Time-Frequency Analysis: (2 weeks)

We will introduce the ideas of signal processing, filtering, time-frequency representations. Our application will be largely to problems in signal processing, denoising and noise reduction.

(2) Dimension Reduction:  (2 weeks)

These methods are practical attempts to reduce the dimensionality of the data as well as infer statistically meaningful trends in what otherwise appears to be noisy data.

(3) Classical Regression:  (2 weeks)

Classical regression methods are fundamental tools for predicting a continuous response variable   from one or more continuous predictors. In this unit, we will study linear and regularized regression models, including least squares, ridge regression, and lasso.

(4) Clustering and Classification:  (1 week)

These methods infer discrete structure from continuous data. We will cover supervised classification techniques for assigning observations to predefined categories, as well as unsupervised clustering methods for discovering groupings in data.

(5) Deep Neural Networks (3 weeks)

These methods are for building nonlinear models that learn from data and then able to perform

various tasks such as clustering, prediction, classification. We will cover how to construct, train and validate such models and apply them to problems of classification ( general data, images) and signal prediction.

Classroom technology:

Please make sure you have access to each of these platforms.

We will use Canvas to manage the course and to release HWs and grades.

We will use grade scope for grading. Class code: 5DK2EV

We will use piazza as our class discussion board. Class code: tenzra1jf9m

Piazza  is  an  excellent  resource  for  pooling  questions  and  learning  from  one  another.  I  highly encourage  you  to  ask  and  answer  questions  about  your  homework  on  Piazza.  You  can  do  so anonymously if you wish. I greatly prefer the use of Piazza over emails, since it is highly likely that others will benefit from answers to your questions. Questions will receive an answer within 36 hours.

Assessment:

●    Assessment for this course is based entirely on projects. There will be no exam during the final exam period (MyUW should say “no traditional final exam”. )

● There will be 5 projects, each worth 20 points

● Each project has 3 components:

○ (75%) Report

○ (15%)  Quiz

○ (10%) Code Checkpoint

See the syllabus sections on homework for more detail.

What is my grade?

We will use a linear grading scheme based on total percentage points from the above rubric. your grade = min{  4*percentage + 0.2, 4 }

Here’s an example conversion table:

All grades will be rounded to the nearest first decimal. For example 3.92 gets rounded down to 3.9 while 3.75 gets rounded up to 3.8.

If the class average is below 3.6 all grades will be shifted up to match that number. For example, if the class average is 3.4 at the end of the quarter then all grades will get bumped up by 0.2.

Homework Instructions

During the quarter, you will receive 5 homework projects that you will turn in via Canvas. Each

homework project will be worth 20 points. Each project has three components: A report (15 points), a homework quiz (3 points), and a code checkpoint (2 points)

Homework Reports (15 points each)

.      A PDF file of a maximum of 6 pages including references Minimum font size of 10pts and margins of 1 in on A4 or standard letter size paper.

.     You do not need to include your code in the report but need to upload it separately along with the PDF report.

.      Formatting: Your report should be formatted as follows:

o Title/author/abstract: Title, author/address lines, and short (100 words or less) abstract. This is not meant to be a separate title page.

o 1. Introduction and Overview

o 2. Theoretical Background

o 3. Algorithm Implementation and Development

o 4. Computational Results

o 5. Summary and Conclusions

o References

.     Typsetting: Using LaTex is recommended ( Overleaf . is great) to prepare your reports. You are also welcome to use Microsoft Word or any other software that properly typesets mathematical equations.

.     Grading: Your  homework will  be graded  based on how completely you solved it as well as neatness and little things like: did you label your graphs and include figure captions. Reports will be graded for the overall layout and specific technical components.

.     Collaboration Policy: Collaboration is encouraged on homework, but each student must turn in their  own  work. Your  solutions  should  be  written  up  in  your  own  words,  so  no  two homeworks should be identical. If you make use of outside resources, be sure to include relevant citations in an acknowledgements section at the bottom of your report.

Homework Code Checkpoint (2 points each)

Each project will include a code checkpoint, due approximately one week before the full assignment. The purpose of the checkpoint is to ensure that you are making steady progress and to help identify any issues early.

For each checkpoint, you will submit your code in an intermediate state. Submissions that demonstrate meaningful progress will receive full credit. (1/3 of the code required for the full assignment will suffice)

Homework Quiz (3 points each)

Along with each project, you will complete a short Canvas quiz consisting of three multiple choice questions related to the homework material. The quiz will be assigned on the same day as the code checkpoint. You will have 24 hours to complete the quiz once it becomes available.

Homework Advice

.      Use  a  professional-grade word  processor  (Latex (recommended) or  Microsoft  Word, for example). For equations: Latex is state-of-the-art, but Word also has a decent equation editor.

.     Read  python documentation. Applying  mathematics through existing software libraries is a core skill  in applied  mathematics. You  are  expected to  rely  on  official  documentation to understand functionality, assumptions, and proper usage.

.      Label all of your graphs, figures, and tables, and include a brief caption. All graphs, figures, and tables should be referenced and discussed in the main text.

.     Label/number all equations that are referenced in the text. If an equation is not referenced later in the text it can be left without a label/number.

.      Provide  references to  scientific  documents  such  as  papers,  books,  arXiv  preprints  where appropriate. Avoid online references such as Wikipedia.

.     Always spell check twice before submitting.

Late Homework Policy

Homework 1-4: Late reports are subject to a 2 points/day penalty up to five days. They will be no  longer be accepted afterwards. For example, if your report is three days late and you managed to get 16/20, your final grade will be 16 − 6 = 10. Please take into account that you will lose 2% of your overall course grade for each day the report is late. So be careful.

Homework 5: The last homework assignment may not be turned in late.

Code checkpoints and Homework quizzes may not be submitted late.