Jose.morales: /* Mathematical Physics II - MAT4XXX/5XXX */

2025-01-24T21:54:08Z

Mathematical Physics II - MAT4XXX/5XXX

Jose.morales: Created page with "=Mathematical Physics II - MAT4XXX/5XXX= ==Course description== The course intends to be a basic introduction to the mathematical and computational techniques in applied math..."

2025-01-24T20:28:48Z

Created page with "=Mathematical Physics II - MAT4XXX/5XXX= ==Course description== The course intends to be a basic introduction to the mathematical and computational techniques in applied math..."

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=Mathematical Physics II - MAT4XXX/5XXX=

==Course description==
The course intends to be a basic introduction to the mathematical
and computational techniques in applied mathematics, computational science & engineer�ing, and data science & machine learning. This course will stress then how the methods of
mathematical modeling in the STEM disciplines have transitioned from the analytical (as in
Theoretical Physics) to the numerical (as in traditional methods in Computational Science
and Engineering) and more recently to Data-based methods (as in current developments in
Data Science and Machine Learning). The student will acquire the basic skills needed broadly
in Computational Science and Engineering, of which Computational Physics, Data Science,
Machine Learning, and Numerical Modeling in the Mathematical Sciences are a subset.

==Catalog entry==

''Prerequisite'':
Calculus III [[MAT2214]] and Differential Equations I [[MAT3613]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

''Content'':
1. Computational Science, Engineering, and Mathematics
(a) Linear Algebra and Computational Science & Engineering
(b) Applied Math and Computational Science & Engineering
(c) Fourier Series and Integrals
(d) Laplace Transform and Spectral Methods
(e) Initial Value Problems
(f) Conjugate Gradients and Krylov Subspaces
(g) Minimum Principles
2. Data Science and Machine Learning: a Mathematical Perspective
(a) Principal Components and the Best Low Rank Matrix
(b) Randomized Linear Algebra
(c) Low Rank and Compressed Sensing
(d) Markov Chains
(e) Stochastic Gradient Descent and ADAM
(f) Introduction to Machine Learning: Neural Networks

'''Textbooks:'''

* Strang, G. Computational Science & Engineering. USA, Wellesley-Cambridge, 2007.
* Strang, G. Linear Algebra and Learning from Data. Wellesley-Cambridge Press, 2019.

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week 1
||
*
||
Strang's 4 special matrices
||

||
*
|-
|Week 2
||
*
||
Differences, Derivatives, BC. Gradient, Divergence. Laplace equation.
||

||
*
|-
|Week 3
||
*
||
Inverses. Positive Definite Matrices
||

||
*
|-
|Week 4
||
*
||
Stiffness Matrices. Oscillations & Newton's Laws.
||

||
*
|-
|Week 5
||
*
||
Graph Models. Networks. Clustering and k-means.
||

||
*
|-
|Week 6
||
*
||
Fourier Series. Chebyshev, Legendre, and Bessel
||

||
*
|-
|Week 7
||
*
||
Fast Fourier Transform (FFT). Convolution and Signal Processing.
||

||
*
|-
|Week 8
||
*
||
Fourier Integrals. Deconvolution, Integral Equations. Wavelets, Signal Processing.
||

||
*
|-
|Week 9
||
*
||
Computational implementation of Laplace and z- Transforms. Spectral Methods.
||

||
*
|-
|Week 10
||

||
Finite Difference for ODEs. Accuracy & Stability. Conservation Laws, diffusion, fluids
||

||
*
|-
|Week 11
||
*
||
Elimination with reordering, multigrid methods, conjugate gradients, Krylov subspaces
||

||
*

|-
|Week 12
||

||
Regular. least sq. Linear programming. Adjoint. Stoch. Gradient Descent. ADAM.
||
*
||
*
|-
|Week 13
||
*
||
Matrix-matrix Multiplication. 4 Fundamental Subspaces. Orthogonal Matrices. Best low rank matrix. Rayleigh quotients. Factoring matrices and tensors.
||

||
*
|-
|Week 14
||
*
||
Randomized Linear Algebra. Low rank signals. Singular values. Compressed sensing. Covariance Matrices. Multivariate Gaussian. Weighted least squares. Markov chains. Neural Networks. Backpropagation. Machine Learning.
||
*
||
*
|}

@@ Line 1: / Line 1: @@
-=Mathematical Physics II - MAT4XXX/5XXX=
+=Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX=
 ==Course description==
-The course intends to be a basic introduction to the mathematical
+This course will be an introduction accessible and welcoming to all STEM students. No prior quantum mechanics courses are expected since all the principles and techniques of quantum information will be taught during the course. The focus will be on qubits, entanglement, and decoherence, three key building blocks of quantum computing.
 ==Catalog entry==
 ''Prerequisite'':
-Calculus III [[MAT2214]] and Differential Equations I [[MAT3613]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.
+Linear Algebra [[MAT2233]] or Applied Linear Algebra [[MAT2253]], or equivalent (can be waived with approval of instructor), with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.
 ''Content'':
-. Computational Science, Engineering, and Mathematics
+Foundations of quantum mechanics such as unitary time evolution, entanglement, and the EPR paradox approached from the information perspective, and quantum entropy. Information and its encoding into physical systems such as photons, atoms, and superconducting circuits.
-(a) Linear Algebra and Computational Science & Engineering
+Quantum control using quantum logic gates, providing a foundation for quantum programming.
-(b) Applied Math and Computational Science & Engineering
+Applications: quantum teleportation, quantum cryptography, quantum computing.
-'''Textbooks:'''
+'''Textbook:'''
@@ Line 50: / Line 29: @@
+*
 ||
-Strang's 4 special matrices
+An overview of quantum computing and information.
 ||
@@ Line 60: / Line 39: @@
+*
 ||
-Differences, Derivatives, BC. Gradient, Divergence. Laplace equation.
+Classical Information Theory. Connection between information and thermodynamics
 ||
@@ Line 70: / Line 49: @@
+*
 ||
-Inverses. Positive Definite Matrices
+Communications Theory. Physical qubits: spinning particles and photons
 ||
@@ Line 80: / Line 59: @@
+*
 ||
-Stiffness Matrices. Oscillations & Newton's Laws.
+Operators in Quantum Mechanics. Classical cryptography
 ||
@@ Line 90: / Line 69: @@
+*
 ||
-Graph Models. Networks. Clustering and k-means.
+Quantum cryptography. Entanglement.
 ||
@@ Line 100: / Line 79: @@
+*
 ||
-Fourier Series. Chebyshev, Legendre, and Bessel
+Mixed states and the density operator. Local measurements & open quantum systems.
 ||
@@ Line 110: / Line 89: @@
+*
 ||
-Fast Fourier Transform (FFT). Convolution and Signal Processing.
+Quantum non-locality and the Einstein-Podolsky-Rosen paradox
 ||
-−
 ||
+*
@@ Line 120: / Line 99: @@
+*
 ||
-Fourier Integrals. Deconvolution, Integral Equations. Wavelets, Signal Processing.
+Bell’s inequality. Quantum dense coding. Quantum teleportation
 ||
@@ Line 130: / Line 109: @@
+*
 ||
-Computational implementation of Laplace and z- Transforms. Spectral Methods.
+Quantum non-locality and the Einstein-Podolsky-Rosen paradox
 ||
@@ Line 140: / Line 119: @@
 ||
-Finite Difference for ODEs. Accuracy & Stability. Conservation Laws, diffusion, fluids
+Quantum computation.
 ||
@@ Line 150: / Line 129: @@
+*
 ||
-Elimination with reordering, multigrid methods, conjugate gradients, Krylov subspaces
+Von Neumann measurements
 ||
@@ Line 161: / Line 140: @@
 ||
-Regular. least sq. Linear programming. Adjoint. Stoch. Gradient Descent. ADAM.
+Many-worlds interpretation of quantum mechanics.
 ||
+*
@@ Line 171: / Line 150: @@
+*
 ||
-Matrix-matrix Multiplication. 4 Fundamental Subspaces. Orthogonal Matrices. Best low rank matrix. Rayleigh quotients. Factoring matrices and tensors.
+Selected topic 1.
 ||
@@ Line 181: / Line 160: @@
+*
 ||
- Randomized Linear Algebra. Low rank signals. Singular values. Compressed sensing. Covariance Matrices. Multivariate Gaussian. Weighted least squares. Markov chains. Neural Networks. Backpropagation. Machine Learning.
+Presentations by students
 ||
+*

MAT5XXX - Revision history

Jose.morales: /* Mathematical Physics II - MAT4XXX/5XXX */

Jose.morales: Created page with "=Mathematical Physics II - MAT4XXX/5XXX= ==Course description== The course intends to be a basic introduction to the mathematical and computational techniques in applied math..."