Tentative Schedule - ESE 2030 📏

Course Outline and Schedule¶

Please note that this is a tentative outline, and that the topics, their components, and their order may be adjusted or removed during the semester. Similarly, dates for homework assignments and midterms may be adjusted as needed.

Table 1:Tentative Course Outline and Schedule

Week	Date	Topics	Homework	Case studies
1	8/27	INTRO / MOTIVATIONS / SETTING THE STORYLINE
1	8/29	MATH 1410 REVISIT 1: SYSTEMS OF LINEAR EQUATIONS, VECTORS, MATRICES, GAUSS ELIMINATION, LU-FACTORIZATION		NETWORK FLOW
2	9/3	MATH 1410 REVISIT 2: PIVOTS+PERMUTATIONS, MATRIX INVERSES (GAUSS-JORDAN), GENERAL LIN SYSTEMS		NETWORK FLOW
2	9/5	VECTOR SPACES 1: DEFINITION, SUBSPACES, SPAN AND LINEAR INDEPENDENCE, BASIS AND DIMENSION	Hw 1 out	NETWORK FLOW REVISITED STEERING A MOBILE ROBOT
3	9/10	VECTOR SPACES 2: BRIEF INTERLUDE: MATRIX TRANSPOSE, THE FUNDAMENTAL MATRIX SUBSPACES (KERNEL, IMAGE, SUPERPOSITION, ADJOINT SYSTEMS, FUND. THM OF LINALG)		NETWORK FLOW REVISITED STEERING A MOBILE ROBOT
3	9/12	VECTOR SPACES 3: CATCH UP AND APPLICATIONS TO CIRCUITS	Hw 2 out, Hw 1 in
4	9/17	INNER PRODUCTS & NORMS: DEFINITION, INEQUALITIES, NORMS		ATTENTION MECHANISM (BASICS) AND COSINE SIMILARITY IN TRANSFORMER EMBEDDING SPACE
4	9/19	APPLICATION: K-MEANS AND CLUSTERING	Hw 3 out, Hw 2 in	K-MEANS FOR MNIST HANDWRITING RECOGNITION AND COLOR COMPRESSION
5	9/24	ORTHOGONALITY: ORTHONORMAL BASES, GRAM-SCHMIDT, ORTHOGONAL MATRICES (QR-FACTORIZATION?), ORTHOGONAL PROJECTIONS & SUBSPACES (ORTHOGONALITY OF THE FUNDAMENTAL MATRIX SUBSPACES AND THE FREDHOLM ALTERNATIVE)
5	9/26	LEAST SQUARES 1: SYMMETRIC AND PSD MATRICES & MINIMIZING QUADRATIC FUNCTIONS	STUDY BREAK, Hw 3 in	APPLICATIONS TO MACHINE LEARNING AND DATA SCIENCE
6	10/1	MIDTERM 1
6	10/3	FALL BREAK!
7	10/8	LEAST SQUARES 2: LEAST SQUARES, DATA FITTING, & INTERPOLATION, LINEARLY CONSTRAINED LEAST SQUARES		APPLICATIONS TO MACHINE LEARNING AND DATA SCIENCE
7	10/10	LINEAR & AFFINE FUNCTIONS, LINEAR TRANSFORMATIONS, AND LINEAR SYSTEMS	Hw 4 out	WORLD, BODY, AND CAMERA FRAMES. COMPUTER GRAPHICS
8	10/15	LINEAR DYNAMICAL SYSTEMS (MOTIVATION, REMINDER OF SCALAR SOLUTION), DETERMINANTS, EIGVALS+VECS, BASES + DIAGONALIZATION		RLC CIRCUITS, DESIGNING AN AUTOPILOT
8	10/17	LINEAR DYNAMICAL SYSTEMS (MOTIVATION, REMINDER OF SCALAR SOLUTION), DETERMINANTS, EIGVALS+VECS, BASES + DIAGONALIZATION	Hw 5 out, Hw 4 in	RLC CIRCUITS, DESIGNING AN AUTOPILOT
9	10/22	REPEATED & COMPLEX EIGENVALUES, JORDAN CANONICAL FORM, GENERAL SOLUTION, MATRIX EXPONENTIAL, CONNECTION TO PREVIOUS SOLUTIONS		RLC CIRCUITS, DESIGNING AN AUTOPILOT
9	10/24	INHOMOGENEOUS SYSTEMS, CAYLEY-HAMILTON, INVARIANT SUBSPACES	Hw 6 out, Hw 5 in
10	10/29	LINEAR ITERATIVE SYSTEMS, MATRIX NORMS AND CONVERGENCE, MARKOV PROCESSES, POPULATION DYNAMICS, PERRON-FROBENIUS		PAGERANK, MARKOV CHAINS & BASEBALL STATISTICS
10	10/31	EIGVALS OF SYMMETRIC MATRICES, SPECTRAL THEOREM, QUADRATIC FORMS, POSITIVE DEFINITE MATRICES, OPTIMIZATION PRINCIPLE FOR EIGENVALUES	Study Break, Hw 6 in
11	11/5	INTRODUCTION TO GRAPH THEORY AND CONSENSUS PROTOCOLS		OPINION DYNAMICS (SOCIAL MEDIA/CONSENSUS)
11	11/7	MIDTERM 2
12	11/12	SINGULAR VALUE DECOMPOSITION: APPLICATIONS TO COVARIANCE MATRICES, SPECTRAL CLUSTERING (FORESHADOW SVD + PCA)
12	11/14	APPLICATIONS OF SVD 1: PCA, Fundamental Theorem of PCA	Hw 7 out	COMPRESSION: EIGENFACES
13	11/19	APPLICATIONS OF SVD 2: Best Rank-K approximation, RECOMMENDERS, RANKINGS		RANKING: SPORTS TEAMS, RECOMMENDER SYSTEMS
13	11/21	INTRO TO OPTIMIZATION, GRADIENT DESCENT & NEWTON’S METHOD	Hw 8 out, Hw 7 in	DEEP LEARNING
14	11/26	STOCHASTIC GRADIENT DESCENT, BACKPROPAGATION, AND START ON MULTILAYER PERCEPTRONS		DEEP LEARNING
14	11/28	THANKSGIVING
15	12/3	A SHALLOW INTRODUCTION TO DEEP LEARNING		TRAINING A DEEP NETWORK FOR IMAGE CLASSIFICATION
15	12/5	REVIEW/CATCH UP	Hw 8 in

ESE 2030 - Linear Algebra with Applications to Engineering and AI

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