Mathematics
Honours
Honours in Pure Mathematics is embedded within the Bachelor of Advanced Studies. Students are required to complete four 6credit points of coursework units and successfully undertake a 24credit point major research project in a specialised area of pure mathematics. This is conducted under the direction of a supervisor who is an expert in the selected topic and who guides the research throughout the year.
To be eligible students need to complete a major that is relevant to the research project undertaken. Admittance into the program is determined by the Faculty of Science as well as the honours coordinator.
Honours Coordinator:
Professor Laurentiu Paunescu
Errata
Item  Errata  Date 

1. 
Prohibitions have been added to the follow unit. It now reads: MATH4063 Dynamical Systems and Applications N: MATH3063 or MATH3963. 
9/3/2021 
2. 
The following unit has had a new 2021 session added: AMSI4001 AMSI Summer School Session: Semester 2 (S2C) 
22/6/2021 
Unit of study  Credit points  A: Assumed knowledge P: Prerequisites C: Corequisites N: Prohibition  Session 

MATHEMATICS (HONOURS) (PURE) 

The Bachelor of Advanced Studies (Honours) (Mathematics (Pure)) requires 48 credit points from this table including:  
(i) 6 credit points of 4000level Honours coursework selective units from List 1, and  
(ii) 6 credit points of 4000level Honours coursework selective units from List 2, and  
(iii) 12 credit points of 4000level and 5000level Honours coursework selective units from List 1, List 2, List 3, List 4 or List 5  
– a maximum of 6 credit points of which may be from List 3, and  
– a maximum of 6 credit points of which may be from List 4, and  
(iv) 24 credit points of 4000level Honours research project units  
Honours Coursework Selective 

List 1 

MATH4311 Algebraic Topology 
6  A Familiarity with abstract algebra and basic topology, e.g., (MATH2922 or MATH2961 or equivalent), (MATH3961 or equivalent) and (MATH2923 or equivalent). 
Semester 2 
MATH4312 Commutative Algebra 
6  A Familiarity with abstract algebra, e.g., MATH2922 or equivalent. 
Semester 2 
MATH4314 Representation Theory 
6  A Familiarity with abstract algebra, specifically vector space theory and basic group theory, e.g., MATH2922 or MATH2961 or equivalent. N MATH3966 
Semester 1 
List 2 

MATH4313 Functional Analysis 
6  A Real Analysis (e.g., MATH2X23 or equivalent), and, preferably, knowledge of Metric Spaces. 
Semester 1 
MATH4315 Variational Methods This unit of study is not available in 2021 
6  A Assumed knowledge of MATH2X23 or equivalent; MATH4061 or MATH3961 or equivalent; MATH3969 or MATH4069 or MATH4313 or equivalent. That is, real analysis, basic functional analysis and some acquaintance with metric spaces or measure theory. 
Semester 2 
List 3 

Students select a 4000level or 5000level unit from a School other than the School of Mathematics and Statistics.  
List 4 

Students select a 5000level unit from the School of Mathematics and Statistics.  
List 5 

AMSI4001 AMSI Summer School 
6  A Completed a first degree with a major in Mathematics, Statistics, Financial Mathematics and Statistics, Data Science or equivalent Note: Department permission required for enrolment This unit has been designed to enable University of Sydney students to continue to take advantage of the premier Mathematics and Statistics summer school held in Australia. The University of Queensland and Melbourne already offer similar shell units to their honours and masters students respectively. 
Intensive February 
MATH4061 Metric Spaces 
6  A Real analysis and vector spaces. For example (MATH2922 or MATH2961) and (MATH2923 or MATH2962) P An average mark of 65 or above in 12cp from the following units (MATH2X21 or MATH2X22 or MATH2X23 or MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979) N MATH3961 
Semester 1 
MATH4062 Rings, Fields and Galois Theory 
6  P (MATH2922 or MATH2961) or a mark of 65 or greater in (MATH2022 or MATH2061) or 12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979) N MATH3062 or MATH3962 
Semester 1 
MATH4063 Dynamical Systems and Applications 
6  A Linear ODEs (for example, MATH2921), eigenvalues and eigenvectors of a matrix, determinant and inverse of a matrix and linear coordinate transformations (for example, MATH2922), Cauchy sequence, completeness and uniform convergence (for example, MATH2923) P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] 
Semester 1 
MATH4068 Differential Geometry 
6  A Vector calculus, differential equations and real analysis, for example MATH2X21 and MATH2X23 P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] N MATH3968 
Semester 2 
MATH4069 Measure Theory and Fourier Analysis 
6  A (MATH2921 and MATH2922) or MATH2961 P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from the following units (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] N MATH3969 
Semester 2 
MATH4071 Convex Analysis and Optimal Control This unit of study is not available in 2021 
6  A MATH2X21 and MATH2X23 and STAT2X11 P [A mark of 65 or above in 12cp of (MATH2XXX or STAT2XXX or DATA2X02)] or [12cp of (MATH3XXX or STAT3XXX)] N MATH3971 
Semester 1 
MATH4074 Fluid Dynamics 
6  A (MATH2961 and MATH2965) or (MATH2921 and MATH2922) P (A mark of 65 or above in 12cp of MATH2XXX ) or (12cp of MATH3XXX ) N MATH3974 
Semester 1 
MATH4076 Computational Mathematics 
6  A (MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65) P [A mark of 65 or above in (12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] or (12cp of MATH3XXX) 
Semester 1 
MATH4077 Lagrangian and Hamiltonian Dynamics 
6  A 6cp of 1000 level calculus units and 3cp of 1000 level linear algebra and (MATH2X21 or MATH2X61) P (A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 orMATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3978 or MATH3979)] N MATH3977 
Semester 2 
MATH4078 PDEs and Applications 
6  A (MATH2X61 and MATH2X65) or (MATH2X21 and MATH2X22) P [A mark of 65 or greater in 6cp from (MATH2X21 or MATH2X65 or MATH2067) and a mark of 65 or greater 6cp from (MATH2X22 or MATH2X61)] or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3979)] N MATH3078 or MATH3978 
Semester 2 
MATH4079 Complex Analysis 
6  A Good knowledge of analysis of functions of one real variable, working knowledge of complex numbers, including their topology, for example MATH2X23 or MATH2962 or MATH3068 P (A mark of 65 or above in 12cp of MATH2XXX) or (12cp of MATH3XXX) N MATH3979 or MATH3964 
Semester 1 
MATH4411 Applied Computational Mathematics 
6  A A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful. 
Semester 1 
MATH4412 Advanced Methods in Applied Mathematics 
6  A A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful. 
Semester 2 
MATH4413 Applied Mathematical Modelling This unit of study is not available in 2021 
6  A MATH2X21 and MATH3X63 or equivalent. That is, a knowledge of linear and simple nonlinear ordinary differential equations and of linear, second order partial differential equations. 
Semester 1 
MATH4414 Advanced Dynamical Systems This unit of study is not available in 2021 
6  A Assumed knowledge is vector calculus (e.g., MATH2X21), linear algebra (e.g., MATH2X22), dynamical systems and applications (e.g., MATH4063 or MATH3X63) or equivalent. Some familiarity with partial differential equations (e.g., MATH3978) and mathematical computing (e.g., MATH3976) is also assumed. 
Semester 2 
MATH4511 Arbitrage Pricing in Continuous Time 
6  A Familiarity with basic probability (eg STAT2X11), with differential equations (eg MATH3X63, MATH3X78) and with basic numerical analysis and coding (eg MATH3X76), achievement at credit level or above in MATH3XXX or STAT3XXX units or equivalent. 
Semester 1 
MATH4512 Stochastic Analysis 
6  A Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent. 
Semester 2 
MATH4513 Topics in Financial Mathematics 
6  A Students are expected to have working knowledge of Stochastic Processes, Stochastic Calculus and mathematical methods used to price options and other financial derivatives, for example as in MATH4511 or equivalent 
Semester 2 
STAT4021 Stochastic Processes and Applications 
6  A STAT2011 or STAT2911, and MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 or equivalent. That is, students are expected to have a thorough knowledge of basic probability and integral calculus and to have achieved at credit level or above in their studies in these topics. N STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT3921. 
Semester 1 
STAT4022 Linear and Mixed Models 
6  A Material in DATA2X02 or equivalent and MATH1X02 or equivalent; that is, a knowledge of applied statistics and an introductory knowledge to linear algebra, including eigenvalues and eigenvectors. N STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904. 
Semester 1 
STAT4023 Theory and Methods of Statistical Inference 
6  A STAT2X11 and (DATA2X02 or STAT2X12) or equivalent. That is, a grounding in probability theory and a good knowledge of the foundations of applied statistics. N STAT3013 or STAT3913 or STAT3023 or STAT3923 
Semester 2 
STAT4025 Time Series 
6  P STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933) N STAT3925 
Semester 1 
STAT4026 Statistical Consulting 
6  P At least 12cp from STAT2X11 or STAT2X12 or DATA2X02 or STAT3XXX N STAT3926 
Semester 1 
STAT4027 Advanced Statistical Modelling 
6  A A three year major in statistics or equivalent including familiarity with material in DATA2X02 and STAT3X22 (applied statistics and linear models) or equivalent P (STAT3X12 or STAT3X22 or STAT4022) and (STAT3X13 or STAT3X23 or STAT4023) 
Semester 2 
STAT4028 Probability and Mathematical Statistics 
6  A STAT3X23 or equivalent: that is, a sound working and theoretical knowledge of statistical inference. N STAT4528 
Semester 1 
STAT4528 Probability and Martingale Theory 
6  A STAT2X11 or equivalent and STAT3X21 or equivalent; that is, a good foundational knowledge of probability and some acquaintance with stochastic processes. N STAT4028 
Semester 1 
Honours Core Research Project 

PMAT4103 Pure Mathematics Honours Project A 
6  Semester 1 Semester 2 

PMAT4104 Pure Mathematics Honours Project B 
6  C PMAT4103 
Semester 1 Semester 2 
PMAT4105 Pure Mathematics Honours Project C 
6  C PMAT4104 
Semester 1 Semester 2 
PMAT4106 Pure Mathematics Honours Project D 
6  C PMAT4105 and SCIE4999 
Semester 1 Semester 2 
SCIE4999 Final Honours Mark 
Semester 1 Semester 2 