Course Syllabus

Below is a syllabus template that includes WSU's required syllabus elements. Please complete all items highlighted in yellow. 

 

Mathematical foundations of AI

Data 461

Semester and Year [tbd]

3 Credits

Prerequisites: DATA 121 or MATH 171  

Course Details

Day and Time: [tbd]

Meeting Location: [tbd]

 

Instructor Contact Information

Instructor Name: [tbd]

Instructor Contact Information: [office location, phone, email] [tbd]

Instructor Office Hours: [click here for best practices] [tbd]

 

TA Name: [tbd]

TA Contact Information: [office location, phone, email]: [tbd]

TA Office Hours: [click here for best practices] [tbd]

 

Course Description

The course will cover the following topics as foundations of AI: 

  • Linear algebra, matrix calculus, and optimization.
  • Graphs theory and graph neural networks and dimension reduction and manifold learning.
  • Function space associated with AI models and their properties, and kernel methods and associated AI models
  • Probabilistic formulation and decision theoretic of AI models and their performances.
  • Ethics of AI

 

Course Materials 

Books: Mathematics for Machine Learning by Deisenroth et al. Available from Amazon.com ($45) or in free pdf online at https://statlearning.com/ 

Other Materials: None

Fees: None

Student Learning Outcomes (SLOs) [add more lines if necessary]

Course Learning Outcomes

(students will be able to:)

 Activities Supporting the Learning Outcomes

Be able to understand and apply basic concepts in linear algebra

Week 1-3

Be able to understand and apply basic concepts of vector calculus and matrix calculus to optimization and study properties of certain optimization techniques

Week 4-6

Be able to apply graphical neural networks and conduct dimension reduction.

Weeks 7-9

Be able to understand function space generated by an AI model and their symmetric properties, and apply kernel methods

Week 10-11

Be able to understand decision theoretic formulation of AI models and their performances

Weeks 12

Be able to apply convolutional neural networks and transformers

Weeks 13

Be able to understand the ethics and societal impacts of AI

Weeks 14

 

Assessment of the Learning Outcomes

Students’ learning outcomes will be accessed by a combination of homework assignments, exams, and projects. Detailed information is given by the following.
Make-up exams:

Make-up exams will be allowed on a case-by-case basis and will be given to accommodate university conflicts, illness or other unforeseen emergencies.  Students must let the instructor know, as soon as possible, that they will not be able to take the scheduled exam.  Make-up exams must be completed before the WSU official final exam date(s) for the semester of the course and within a reasonable period after they were originally scheduled.
Homework:

Approximately 5 homework assignments will be given during the semester.  These will come from problems provided by reference books or materials discussed in the lectures. Homework assignments will primarily consist of methodological and programming exercises. Please submit answers to HW assignments with necessary supporting computer codes and organize them. Late homework will only be accepted under extenuating circumstances, such as an extended illness.  
Written Projects:

One final project will be assigned during the semester. Each project will consist of 4 components: (1) a typed write-up that contains 5 components:  introduction, methods used to conduct the analysis, results of the analysis, conclusions from and discussion on the analysis, and a reference section; (2) computer codes used to conduct the analysis; (3) most relevant outputs from the analysis, which can be incorporated in component (1); (4) a detailed description of the contribution of each member of the group towards the project.  Each project can be completed by up to 2 students.

Course Schedule

[Please note that a WSU semester is 15 weeks + Thanksgiving/Spring Break. The schedule below does not include the break.]
Dates Lesson Topic Topics Materials

Week 1
[dates]

  Introduction
  • Overview of AI and its mathematical foundations
  • Key mathematical concepts in AI
  • Course logistics and expectations
  •   Lecture notes
  • Supplementary: Mathematics for Machine Learning by Deisenroth et al. (Ch. 1)
Week 2
[dates]		   Linear Algebra I
  •  Vectors, matrices, and operations
  • Matrix decomposition: Eigenvalues, eigenvectors, singular value decomposition (SVD)
  • Vector spaces and norms
  •   Linear Algebra and Its Applications by Gilbert Strang
  • Python Libraries: NumPy, Matplotlib
Week 3
[dates]		   Linear Algebra II
  • Matrix calculus
  • Applications in neural networks
  • Numerical stability in matrix operations
  •   Mathematics for Machine Learning by Deisenroth et al. (Ch. 2)
  • Python Libraries: NumPy, SciPy
Week 4
[dates]
   Calculus I – Differentiation   
  • Gradients and partial derivatives
  • Chain rule
  • Gradient descent applications
  
  • Mathematics for Machine Learning by Deisenroth et al. (Ch. 2)
  • Python Libraries: NumPy, SymPy
Week 5
[dates]
   Calculus II – Optimization  
  • Convex functions and optimization landscapes
  • Gradient descent variants
  • Lagrange multipliers
  
  • Convex Optimization by Boyd and Vandenberghe
  • Python Libraries: SciPy 
Week 6
[dates]
   Numerical Methods   
  • Solving equations numerically
  • Stability and convergence
  • Iterative methods for AI
   
  • Numerical Analysis by Burden and Faires
  • Python Libraries: SciPy, NumPy
Week 7
[dates]
   Graph Theory & Network Structures  
  • Graphs, nodes, edges
  • Graph algorithms: shortest path, clustering
  • Applications in AI: Graphical Neural Networks (GNNs), social networks
   
  • Graph Theory by Reinhard Diestel
  • Python Library: NetworkX
Week 8
[dates]
    Dimensionality Reduction   
  • PCA and SVD
  • Manifold Learning
  • Data visualization in high dimensions
   
  • Mathematics for Machine Learning by Deisenroth et al. (Ch. 5)
  • Python Libraries: scikit-learn
Week 9
[dates]
   Midterm Exam and Review   
  • Review Weeks 1–8
  • Midterm assessment
   
Week 10
[dates]
   Symmetry and Transformations   
  • Basic concepts of symmetry and transformations
  • Data augmentation in AI models
  • Equivariance and invariance with simple examples
   
  • Lecture notes
Week 11
[dates]		   Vector and Function Spaces   
  • Hilbert and Banach spaces basics
  • Applications: kernel methods, Fourier transforms
    
  • Functional Analysis by Kreyszig
Week 12
[dates]
  Probability Foundations and Integration   
  • Review of probability concepts (as refresher)
  • Integration as area under curves and in expectation
  • Applications in AI: expected value, loss functions
   
  • Lecture notes with examples in probability and expectations
  • Python Libraries: SciPy, NumPy
Week 13
[dates]
   Special topics  
  • Convolutional neural networks
  • Transformers
   
  • Instructor prepared lecture notes
  • Python Libraries: SciPy, NumPy
Week 14
[dates]
   Ethical and Responsible AI   
  • Ethical challenges, bias, fairness
  • Transparency and explainability
   
  • Ethics of Artificial Intelligence by Bostrom and Yudkowsky
  • Case studies
Week 15
[dates]
   Final Project Presentations  
  • Final project
  

 

 

Expectations for Student Effort 

You are expected to spend a minimum of 9 hours per week for a three-credit course, of which 3 hours are
spent on instructor-led activities (lectures and discussions) and 6 hours are spent on outside activities.
These outside activities include, but are not limited to: reading, studying, problem solving, writing, homework, and other preparations for the course. Achievement of course goals may require more than the minimum time commitment. For the most accurate and up to date information go to Academic Regulations.

 

Grade Distribution

Assignment Breakdown
Type of Assignment (tests, papers, etc) Percent of Overall Grade

Homework

50%

Mid-term exam

20%

Final project

30%

Total

100%

 

Grading Schema
Grade Percent Grade Percent
A 93% - 100% C  73% - 76.99%
A-  90% - 92.99% C- 70% - 72.99%
B+  87% - 89.99% D+ 66% - 69.99%
B 83% - 86.99% D 60% - 65.99%
B- 80% - 82.99% F 0% - 59.99%
C+ 77% - 79.99%  

[Provide information about how grades will be rounded (eg, if 89% earns a B+ and 90% earns an A-, what grade is given to a student with an 89.5?]

Attendance and Make-Up Policy 

Students should make all reasonable efforts to attend all class meetings. However, in the event a student is unable to attend a class, it is the responsibility of the student to inform the instructor as soon as possible, explain the reason for the absence (and provide documentation, if appropriate), and make up class work missed within a reasonable amount of time, if allowed. Missing class meetings may result in reducing the overall grade in the class.

 

Academic Integrity Statement

You are responsible for reading WSU's Academic Integrity Policy, which is based on Washington State law. If you cheat in your work in this class you will:

-Be reported to the Center for Community Standards

-Have the right to appeal my decision

-Not be able to drop the course of withdraw from the course until the appeals process is finished

If you have any questions about what you can and cannot do in this course, ask me.

If you want to ask for a change in my decision about academic integrity, use the form at the Center for Community Standards website. You must submit this request within 21 calendar days of the decision.