Department of Mathematics at UTSA - Recent changes [en]

MAT5283

Jose.iovino — Wed, 25 Mar 2026 01:48:28 GMT

MAT5433

Jose.iovino — Wed, 25 Mar 2026 01:30:36 GMT

MAT5YYY

Jose.iovino — Wed, 25 Mar 2026 00:03:11 GMT

Mathematics of AI - MAT4YYY/5YYY

MAT5433

Jose.iovino — Tue, 24 Mar 2026 23:11:28 GMT

MAT5283

Jose.iovino — Tue, 24 Mar 2026 23:06:09 GMT

MAT 5183

Jose.iovino — Tue, 24 Mar 2026 23:01:36 GMT

Catalog entry

Main Page

Jose.iovino — Tue, 24 Mar 2026 22:58:52 GMT

Graduate Studies

MAT2253

Stephen.pena — Tue, 17 Mar 2026 16:09:06 GMT

moved matrix factorization up

@@ Line 5: / Line 5: @@
 ''Prerequisite'':  Prerequisite: Math 2233 Linear Algebra, Math 2243 Applied Linear Algebra or instructor approval.  , or instructor consent.
-''Contents''
+''Contents'':
 (1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector
 spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor-

@@ Line 1: / Line 1: @@
 == Catalog entry ==
-''Prerequisite'':Discrete Mathematics (MAT 3003) or Real Analysis I (MAT 4213), or instructor consent.
+''Prerequisite'':
 ''Contents''
  The Zermelo-Fraenkel axioms, ordinals and cardinals, the Axiom of Foundation, the Reflection Principle, ordinal-definable sets, relative consistency of the Axiom of Choice, Fraenkel-Mostowski models, relative consistency of the negation of the Axiom of Choice, consistency of the Generalized Continuum Hypothesis.

← Older revision		Revision as of 00:03, 25 March 2026
(One intermediate revision by the same user not shown)
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	''Content'':		''Content'':
	Vectors, matrices and tensors; discrete and continuous probability; random variables and expectation; elements of information theory; basic methods for probabilistic learning (maximum likelihood, Bayesian statistics); supervised and unsupervised learning algorithms; neural networks: feedforward, convolutional, recurrent/recursive; loss functions and gradient-based learning; optimization and regularization methods; algorithm implementations; testing on real-world datasets.		Vectors, matrices and tensors; discrete and continuous probability; random variables and expectation; elements of information theory; basic methods for probabilistic learning (maximum likelihood, Bayesian statistics); supervised and unsupervised learning algorithms; neural networks: feedforward, convolutional, recurrent/recursive; loss functions and gradient-based learning; optimization and regularization methods; algorithm implementations; testing on real-world datasets.
−
−
−	~~== Sample textbook ==~~
−
−	~~[1] Mathematics of Quantum Computing: An Introduction~~
−	~~by Wolfgang Scherer, Springer, 2019.~~

@@ Line 1: / Line 1: @@
 == Catalog entry ==
-''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
+''Prerequisite'':Discrete Mathematics (MAT 3003) or Real Analysis I (MAT 4213), or instructor consent.
 ''Contents''
-(1) Basic counting principles: Permutations, combinations, binomial coefficients, arrangements with repetitions.
+ The Zermelo-Fraenkel axioms, ordinals and cardinals, the Axiom of Foundation, the Reflection Principle, ordinal-definable sets, relative consistency of the Axiom of Choice, Fraenkel-Mostowski models, relative consistency of the negation of the Axiom of Choice, consistency of the Generalized Continuum Hypothesis.

← Older revision		Revision as of 23:06, 24 March 2026
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	''Contents''		''Contents''
−	(This course has been designed for advanced undergraduate students and first year graduate students. The subjects have been developed to include material that is fundamental for contemporary applications of linear algebra like Error-Correcting Codes, Cryptography, Quantum Computing and Quantum Algorithms. Topics include: (1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, ~~isomorphisms~~, Rank-~~Nulity~~ Theorem, Product and Quotient Spaces (3) Matrices and Linear ~~Transformations~~: Matrix representation, change of basis, equivalence of matrices, similarity (4) ~~Eigenvalues~~ and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan ~~Canonical~~ forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz ~~inequality~~, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez ~~Representation~~ Theorem (5) Orthogonality over finite fields	+	(1) Algebraic Structures: rings, matrices, polynomials, fields and finite fields (2) Vector
		+	spaces: subspaces, linear independence, basis, dimension (3) Linear transformations, isomor-
		+	phisms, Rank-Nullity Theorem, Product and Quotient Spaces (3) Matrices and Linear Transfor-
		+	mations: Matrix representation, change of basis, equivalence of matrices, similarity (4) Eigen-
		+	values and Eigenvectors: The Cayley-Hamilton Theorem, Diagonalization and Jordan Canoni-
		+	cal forms (4) Real and Complex Inner Product Spaces: Norm, distances, Cauchy-Schwartz in-
		+	equality, Gram-Schmidt Orthogonalization process, The Projection Theorem, Riez Representa-
		+	tion Theorem (5) Orthogonality over finite fields (6) Multilinear algebra : Bilinear Forms and
		+	Functionals, Tensor product of vector spaces and Matrices.

@@ Line 84: / Line 84: @@
 * [[MAT5283]] Linear Algebra
 * [[MAT5203]] Real Analysis I
-* [[MAT 5173]] Abstract Algebra I
+* [[MAT 5173]] Algebra I
 * [[MAT5603]] Differential Equations I
@@ Line 100: / Line 100: @@
 === Qualifying Exam Track: Algebra-Cryptography  ===
-* [[MAT 5173]] Abstract Algebra I
+* [[MAT 5173]] Algebra I
-* [[MAT 5183]] Abstract Algebra II
+* [[MAT 5183]] Algebra II
 * [[MAT 5123]] Introduction to Cryptography
 * [[MAT 5143]] Cryptography II (Post-Quantum Cryptography)

@@ Line 30: / Line 30: @@
 | 9 || 2.7 || Linear Mappings (examples) ||  ||
 |-
-| 10 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances ||  ||
+| 10 || 4.1 || Determinant and Traces ||  ||
 |-
-| 11 || 3.4 || Angles & orthogonality ||  ||
+| 11 || 4.2 || Eigenvalues & Eigenvectors ||  ||
 |-
-| 12 || 3.5 || Orthonormal Basis ||  ||
+| 12 || 4.3, 4.4 || Matrix Factorization ||  ||
 |-
-| 13 || 3.7 || Inner Product of Functions ||  ||
+| 13 || 3.1, 3.2, 3.3 || Norms, Inner Products, Lengths & Distances ||  ||
 |-
-| 14 || Project 1 ||  ||  ||
+| 14 || 3.4 || Angles & orthogonality ||  ||
 |-
-| 15 || 4.1 || Determinant and Traces ||  ||
+| 15 || 3.5 || Orthonormal Basis ||  ||
 |-
-| 16 || 4.2 || Eigenvalues & Eigenvectors ||  ||
+| 16 || 3.7 || Inner Product of Functions ||  ||
 |-
-| 17 || 4.3, 4.4 || Matrix Factorization ||  ||
+| 17 || Project 1 ||  ||  ||
 |-
 | 18 || 5.1 ||Vector Calculus Intro and Taylor Series ||  ||