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Showing 25 course outlines from 794 matches
401
MATHS 721
: Representations and Structure of Algebras and Groups2025 Semester Two (1255)
Representation theory studies properties of abstract groups and algebras by representing their elements as linear transformations of vector spaces or matrices, thus reducing many problems about the structures to linear algebra, a well-understood theory.
Prerequisite: MATHS 320
402
MATHS 725
: Lie Groups and Lie Algebras2025 Semester Two (1255)
Symmetries and invariants play a fundamental role in mathematics. Especially important in their study are the Lie groups and the related structures called Lie algebras. These structures have played a pivotal role in many areas, from the theory of differential equations to the classification of elementary particles. Strongly recommended for students advancing in theoretical physics and pure mathematics. Recommended preparation: MATHS 333.
Prerequisite: MATHS 320 and 332
403
MATHS 730
: Measure Theory and Integration2025 Semester One (1253)
Presents the modern elegant theory of integration as developed by Riemann and Lebesgue. This course includes powerful theorems for the interchange of integrals and limits, allowing very general functions to be integrated, and illustrates how the subject is both an essential tool for analysis and a critical foundation for the theory of probability. Strongly recommended: MATHS 333
Prerequisite: MATHS 332
404
MATHS 731
: Functional Analysis2025 Semester Two (1255)
Provides the mathematical foundations behind some of the techniques used in applied mathematics and mathematical physics; it explores how many phenomena in physics can be described by the solution of a partial differential equation, for example the heat equation, the wave equation and Schrödinger's equation. Recommended preparation: MATHS 730 and 750.
Prerequisite: MATHS 332 and 333
405
MATHS 740
: Complex Analysis2025 Semester One (1253)
An introduction to functions of one complex variable, including Cauchy's integral formula, the index formula, Laurent series and the residue theorem. Many applications are given including a three line proof of the fundamental theorem of algebra. Complex analysis is used extensively in engineering, physics and mathematics. Strongly recommended: MATHS 333.
Prerequisite: MATHS 332
Restriction: MATHS 341
Restriction: MATHS 341
406
MATHS 761
: Dynamical Systems2025 Semester One (1253)
Mathematical models of systems that change are frequently written in the form of nonlinear differential equations, but it is usually not possible to write down explicit solutions to these equations. This course covers analytical and numerical techniques that are useful for determining the qualitative properties of solutions to nonlinear differential equations.
Prerequisite: B- in both MATHS 340 and 361
407
MATHS 763
: Advanced Partial Differential Equations2025 Semester One (1253)
A study of advanced exact and numerical methods for both linear and non-linear partial differential equations.
Prerequisite: B- in both MATHS 340 and 361
408
MATHS 765
: Mathematical Modelling2025 Semester Two (1255)
Advanced topics in mathematical modelling, including selected topics in a range of application areas, principally taken from the physical and biological sciences.
Prerequisite: At least B- or better in both MATHS 340 and 361
409
MATHS 767
: Inverse Problems and Stochastic Differential Equations2025 Semester One (1253)
Covers stochastic differential equations and inverse problems, including: continuous time processes, random walks and Wiener processes, Itō calculus, and applications of SDEs, Hilbert spaces and linear operator theory, singular value decomposition and pseudoinverses, Tikhonov regularisation, nonlinear problems and iterative methods.
Prerequisite: B- or higher in MATHS 340 and 361
Restriction: MATHS 766, 769, 787
Restriction: MATHS 766, 769, 787
410
MATHS 770
: Advanced Numerical Analysis2025 Semester Two (1255)
Covers the use, implementation and analysis of efficient and reliable numerical algorithms for solving several classes of mathematical problems. The course assumes students have done an undergraduate course in numerical methods and can use Matlab or other high-level computational language.
Prerequisite: B- in MATHS 270, 340 and 361
411
PHYSICS 102
: Basic Concepts of Physics2025 Semester One (1253)
An introduction to the basic principles of physics. Key topics are the physical description of motion, electricity and magnetism. The course focuses on the science of everyday phenomena and the understanding of important physical concepts. This course will equip students with little prior knowledge of physics to succeed in PHYSICS 120 or 160.
Restriction: PHYSICS 103
412
PHYSICS 102
: Basic Concepts of Physics2025 Summer School (1250)
An introduction to the basic principles of physics. Key topics are the physical description of motion, electricity and magnetism. The course focuses on the science of everyday phenomena and the understanding of important physical concepts. This course will equip students with little prior knowledge of physics to succeed in PHYSICS 120 or 160.
Restriction: PHYSICS 103
413
PHYSICS 120
: Advancing Physics 12025 Semester Two (1255)
For students progressing in physical science. Key topics are mechanics, energy, rotation, oscillations, waves and thermodynamics. This is a calculus based course, focusing on fundamental principles, problem solving and hands-on exercises. Prerequisite: PHYSICS 102, or at least 4 credits in the Mechanics (91524) or Waves (91523) standards in NCEA Level 3 Physics and at least 6 credits in the Differentiation (91578) or Integration (91579) standards in NCEA Level 3 Calculus, or equivalent with departmental approval
Restriction: PHYSICS 160
414
PHYSICS 120
: Advancing Physics 12025 Semester One (1253)
For students progressing in physical science. Key topics are mechanics, energy, rotation, oscillations, waves and thermodynamics. This is a calculus based course, focusing on fundamental principles, problem solving and hands-on exercises. Prerequisite: PHYSICS 102, or at least 4 credits in the Mechanics (91524) or Waves (91523) standards in NCEA Level 3 Physics and at least 6 credits in the Differentiation (91578) or Integration (91579) standards in NCEA Level 3 Calculus, or equivalent with departmental approval
Restriction: PHYSICS 160
415
PHYSICS 121
: Advancing Physics 22025 Semester Two (1255)
For students progressing in physical science. Key topics are electrostatics, electromagnetism, circuits, optics, relativity and quantum mechanics. This is a calculus based course, focusing on fundamental principles, problem solving and hands-on exercises. Prerequisite: PHYSICS 120, or 24 credits in the Mechanics (91524), Electricity (91526), Differentiation (91578), Integration (91579) standards in NCEA Level 3 at merit or excellence, or equivalent with departmental approval
Restriction: PHYSICS 150
416
PHYSICS 140
: Digital Fundamentals2025 Semester Two (1255)
An introduction to the physical basis of modern computing for Computer Science students and anyone with an interest in modern Information Technology. Key topics are Boolean Algebra, logic circuits, and digital information processing. Hands-on laboratory work is a key component of the course. No prior electronics or programming knowledge is assumed.
Restriction: PHYSICS 219, 243
417
PHYSICS 140
: Digital Fundamentals2025 Semester One (1253)
An introduction to the physical basis of modern computing for Computer Science students and anyone with an interest in modern Information Technology. Key topics are Boolean Algebra, logic circuits, and digital information processing. Hands-on laboratory work is a key component of the course. No prior electronics or programming knowledge is assumed.
Restriction: PHYSICS 219, 243
418
PHYSICS 160
: Physics for the Life Sciences2025 Semester Two (1255)
Designed for students intending to advance in the biomedical and life sciences, this course is focused on physical principles relevant to biological systems. Key topics are motion, waves, thermal physics, electricity and instrumentation. The course is primarily algebra-based and includes lectures, laboratories and tutorials. Recommended preparation is NCEA Level 2 Physics and Mathematics, or equivalent.
Restriction: PHYSICS 120
419
PHYSICS 201
: Classical and Thermal Physics2025 Semester One (1253)
Classical mechanics and thermal physics. Key topics are linear and rotational motion in three dimensions, fluids, oscillations and mechanical waves, and the laws of thermodynamics. The course will cover both fundamental principles and applied topics, such as planetary dynamics and spacecraft navigation, ultrasound, atmospheric physics and materials science.
Prerequisite: 15 points from PHYSICS 120, 121, 150, 160 and 15 points from ENGSCI 211, MATHS 130, 208, PHYSICS 211
Restriction: PHYSICS 230, 231
Restriction: PHYSICS 230, 231
420
PHYSICS 202
: Electromagnetism2025 Semester Two (1255)
Key topics are electric and magnetic fields, the generation of magnetic fields by currents, the derivation of Maxwell’s equations, the interpretation of light as an electromagnetic wave and polarisation. Both fundamental principles and applied topics, including fibre optics, LEDs, physical optics and interferometers are covered.
Prerequisite: 15 points from PHYSICS 121, 150 and 15 points from ENGSCI 211, MATHS 130, 208, PHYSICS 211
Restriction: PHYSICS 260, 261
Restriction: PHYSICS 260, 261
421
PHYSICS 203
: Relativity and Quantum Physics2025 Semester Two (1255)
Special relativity, quantum mechanics and nuclear physics. Key topics are the Lorentz transformation, mass-energy equivalence, the Schrödinger equation in one dimension, the hydrogen atom, atomic and molecular bonds, isotopes and radioactivity. Both fundamental principles and applied topics, including isotope production, nuclear medicine, and dosimetry are covered.
Prerequisite: 15 points from PHYSICS 121, 150 and 15 points from ENGSCI 211, MATHS 130, 208, PHYSICS 211
Restriction: PHYSICS 250, 251
Restriction: PHYSICS 250, 251
422
PHYSICS 244
: Electronics and Imaging2025 Semester One (1253)
Provides students with skills in electronics and imaging technologies that will support future work in technology-focused careers, experimental science, medical physics, and photonics. Key topics include networks, resonance, amplifiers, semiconductors, Fourier analysis, imaging systems, MRI systems and biomedical imaging.
Prerequisite: 15 points from PHYSICS 120, 121, 140, 160 and 15 points from COMPSCI 120, ENGGEN 150, ENGSCI 111, MATHS 108, 110, 120, 130, 150
Restriction: PHYSICS 240
Restriction: PHYSICS 240
423
PHYSICS 309
: Special Study2025 Semester Two (1255)
Directed study on a topic or topics approved by the Academic Head or nominee.
Prerequisite: 45 points from PHYSICS 201-203, 244
424
PHYSICS 309
: Special Study2025 Semester One (1253)
Directed study on a topic or topics approved by the Academic Head or nominee.
Prerequisite: 45 points from PHYSICS 201-203, 244
425
PHYSICS 309
: Special Study2025 Summer School (1250)
Directed study on a topic or topics approved by the Academic Head or nominee.
Prerequisite: 45 points from PHYSICS 201-203, 244