DATA-461-christina.myers-2025-09-26-12-54-45

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]

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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.