MAT5143 - Revision history

Jose.morales: /* Course description */

2025-01-24T18:26:37Z

Course description

Jose.morales: /* Course description */

2025-01-21T22:34:13Z

Course description

Juan.gutierrez3: Moved content from MAT4143

2023-03-24T15:13:43Z

Moved content from MAT4143

Eduardo.duenez: MAT5143 is Math Physics!

2023-03-23T19:29:55Z

MAT5143 is Math Physics!

Jose.iovino at 17:55, 22 March 2023

2023-03-22T17:55:12Z

Duynguyenvu.hoang: /* Topics List */

2023-03-10T23:07:54Z

Topics List

Duynguyenvu.hoang: /* Topics List */

2023-03-10T23:06:54Z

Topics List

Duynguyenvu.hoang: Created Math Phys page

2023-03-10T23:06:16Z

Created Math Phys page

New page

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
|-
|Week I
||
* Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
||
* [[Order of Differential Equations]]
||
* Integration techniques
:- [[Direct Integration]]
:- [[Integration by Substitution]]
:- [[Integration by Parts]]
:- [[Partial Fractions]]
||
* Explain the basic notion of the order of a differential equation.
|-
}

@@ Line 4: / Line 4: @@
 Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.
-CATALOG ENTRY:
+==Catalog entry==
 '''Textbooks:'''

@@ Line 2: / Line 2: @@
 ==Course description==
-Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding or mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.
+Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding of mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.
 '''Textbooks:'''
@@ Line 12: / Line 17: @@
 * Kreyszig, E. (1989). Introductory Functional Analysis with Applications. Wiley.
 * Methods of Applied Mathematics. Todd Arbogast and Jerry L. Bona. Department of Mathematics, and Institute for Computational Engineering and Sciences, University of Texas at Austin, 2008.
-* P. J. Olver , Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993.
+* P. J. Olver, Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993.
 * Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications

← Older revision		Revision as of 19:29, 23 March 2023
Line 1:		Line 1:
−	~~Introduction to post-quantum Cryptography.~~	+	Mathematical Physics.
−
−
−	~~'''Sample textbook''':~~
−
−	~~[1] Daniel Bernstein, Johannes Buchmann, Erik Dahmen, ''Post-Quantum Cryptography'', Springer, 2010.~~
−
−
−
−
−	~~'''Catalog entry'''~~
−
−	~~''Prerequisite'': Algebra and Number Systems (MAT 1313), or Discrete~~ Mathematical ~~Structures (CS 2233/2231), or instructor consent.~~
−
−	~~''Contents'':~~
−	~~(1) Introduction to post-quantum cryptography.~~
−	~~(2) Quantum computing.~~
−	~~(3) Hash-based Digital Signature Schemes.~~
−	~~(4) Code-based cryptography.~~
−	~~(5) Lattice-based Cryptography~~
−	~~(6) Multivariate Public Key Cryptography.~~
−	~~(7) Homomorphic encryption.~~
−
−
−
−
−
−
−	~~==Topics List==~~
−	~~{\| class="wikitable sortable"~~
−	~~! Week !! Topic !! Chapter 1 from the Bernstein-Johannes Buchmann-Dahmen book !! MAT1313, or CS2233/2231, or instructor consent.~~
−	\|-
−	~~\| 1-3~~
−	~~\|\| [[Introduction to post-quantum cryptography]]~~
−	~~\|\| 1~~
−	~~\|\| MAT1313 or CS2233/2231, or equivalent~~.
−	\|-
−	~~\| 2-4~~
−	~~\|\| [[Quantum computing]]~~
−	~~\|\| 2~~
−	\|\|
−	\|-
−	~~\| 5-6~~
−	~~\|\| [[Hash-based Digital Signature Schemes]]~~
−	~~\|\| 3~~
−	\|\|
−	\|-
−	~~\| 7-8~~
−	~~\|\| [[Code-based cryptography]]~~
−	~~\|\| 4~~
−	\|\|
−	\|-
−	~~\| 9-10~~
−	~~\|\| [[Lattice-based Cryptography]]~~
−	~~\|\| 5~~
−	\|\|
−	\|-
−	~~\| 11-12~~
−	~~\|\| [[Multivariate Public Key Cryptography]]~~
−	~~\|\| 6~~
−	\|\|
−	\|-
−	~~\| 13-end~~
−	~~\|\| [[Homomorphic encryption]]~~
−	\|\|
−	\|\|
−	\|}

@@ Line 1: / Line 1: @@
 ==Topics List==
 {| class="wikitable sortable"
-! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
+! Week !! Topic !! Chapter 1 from the Bernstein-Johannes Buchmann-Dahmen book !! MAT1313, or CS2233/2231, or instructor consent.
 |-
-|Week 1
+|  1-3
-||
+|| [[Introduction to post-quantum cryptography]]
+|| 1
-||
+|| MAT1313 or CS2233/2231, or equivalent.
 |-
+|  2-4

← Older revision		Revision as of 15:13, 24 March 2023
Line 1:		Line 1:
−	Mathematical Physics.	+	=Mathematical Physics - MAT4143/5153=
		+
		+	==Course description==
		+	Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding or mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.
		+
		+	'''Textbooks:'''
		+
		+	* Needham, T. (1997). Visual Complex Analysis. United Kingdom: Clarendon Press.
		+	* Grimshaw, R. (1993). Nonlinear Ordinary Differential Equations (1st ed.). Routledge.
		+	* R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley Classics Library, John Wiley & Sons Inc., New York, 1989.
		+	* Bender, C. and Orszag, S. Advanced Mathematical Methods for Scientists and Engineers. Mc-Graw Hill.
		+	* Kreyszig, E. (1989). Introductory Functional Analysis with Applications. Wiley.
		+	* Methods of Applied Mathematics. Todd Arbogast and Jerry L. Bona. Department of Mathematics, and Institute for Computational Engineering and Sciences, University of Texas at Austin, 2008.
		+	* P. J. Olver , Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993.
		+	* Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications
		+
		+	==Topics List==
		+	{\| class="wikitable sortable"
		+	! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
		+	\|-
		+	\|Week 1
		+	\|\|
		+	*
		+	\|\|
		+	Complex Analysis Part I
		+	\|\|
		+
		+	\|\|
		+	* Definition and algebraic properties of complex numbers, Riemann Sphere, Holomorphic functions and conformal mappings
		+	\|-
		+	\|Week 2
		+	\|\|
		+	*
		+	\|\|
		+	Complex Analysis Part II
		+	\|\|
		+
		+	\|\|
		+	*Integrals in the Complex Plane, Cauchy's theorem, Calculus of Residues
		+	\|-
		+	\|Week 3
		+	\|\|
		+	*
		+	\|\|
		+	Complex Analysis Part III
		+	\|\|
		+
		+	\|\|
		+	* Harmonic functions and Poisson's formula
		+	\|-
		+	\|Week 4
		+	\|\|
		+	*
		+	\|\|
		+	Tensor Calculus Basics I
		+	\|\|
		+
		+	\|\|
		+	* Using indices in three-dimensional cartesian vector analysis, deriving vector identities using index calculus, divergence, grad and curl in index notation, divergence and Stokes' theorem.
		+	\|-
		+	\|Week 5
		+	\|\|
		+	*
		+	\|\|
		+	Tensor Caluclus Basics II
		+	\|\|
		+
		+	\|\|
		+	* Manifolds and coordinate transformations, vector fields, Riemannian geometry, covariant derivatives and Christoffel symbols
		+	\|-
		+	\|Week 6
		+	\|\|
		+	*
		+	\|\|
		+	Applied Functional Analysis Part I
		+	\|\|
		+
		+	\|\|
		+	* Hilbert spaces and inner products, orthogonality and completeness.
		+	\|-
		+	\|Week 7
		+	\|\|
		+	*
		+	\|\|
		+	Applied Functional Analysis Part II
		+	\|\|
		+
		+	\|\|
		+	* Operators in Hilbert spaces, eigenvalue problem, self-adjointness and spectral properties
		+	\|-
		+	\|Week 8
		+	\|\|
		+	*
		+	\|\|
		+	Applied Functional Analysis Part III
		+	\|\|
		+
		+	\|\|
		+	* Examples of Hilbert spaces in quantum mechanics, standard examples such as potential wells and harmonic oscillator
		+	\|-
		+	\|Week 9
		+	\|\|
		+	*
		+	\|\|
		+	Overview about ordinary differential equations I
		+	\|\|
		+
		+	\|\|
		+	* Systems of nonlinear/linear equations, basic existence and uniqueness theorems
		+	\|-
		+	\|Week 10
		+	\|\|
		+
		+	\|\|
		+	Overview about ordinary differential equations II
		+	\|\|
		+
		+	\|\|
		+	* Phase-plane, linearization, stability, chaos
		+	\|-
		+	\|Week 11
		+	\|\|
		+	*
		+	\|\|
		+	PDE's of Mathematical Physics
		+	\|\|
		+
		+	\|\|
		+	* Standard examples, qualitative properties, conservation laws
		+
		+	\|-
		+	\|Week 12
		+	\|\|
		+
		+	\|\|
		+	Introduction to Lie Groups and Symmetries I
		+	\|\|
		+	*
		+	\|\|
		+	* Definition of a Lie group and examples, commutators and Lie brackets, Lie algebras
		+	\|-
		+	\|Week 13
		+	\|\|
		+	*
		+	\|\|
		+	Introduction to Lie Groups and Symmetries II
		+	\|\|
		+
		+	\|\|
		+	* Exponential maps, applications of Lie groups to differential equations, Noether's theorem
		+	\|-
		+	\|Week 14
		+	\|\|
		+	*
		+	\|\|
		+	KdV equation, completely integrable systems
		+	\|\|
		+	*
		+	\|\|
		+	* Soliton solutions, infinite hierarchy of conservation laws
		+	\|}

@@ Line 5: / Line 5: @@
 |Week I
 ||
-* Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
 ||
-* [[Order of Differential Equations]]
 ||
-* Integration techniques
 ||
-* Explain the basic notion of the order of a differential equation.
 |-
+}