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#
Pure Mathematics

##
Honours unit of study table (Table A)

#### Honours coordinator:

Honours in Pure Mathematics is embedded within the Bachelor of Advanced Studies. Students are required to complete four 6-credit points of coursework units following the rules in the Pure Mathematics Honours units of study table and successfully undertake a 24-credit 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.

Honours is available to students who have a completed major in an area relevant to their project and have met the requirements outlined in the resolutions. The candidate is expected to find a prospective supervisor from among the Pure Mathematics staff. Admittance into the program is determined by the Faculty of Science as well as the honours coordinator.

Professor Laurentiu Paunescu

laurentiu.paunescu@sydney.edu.au

## Mathematics (Honours) (Pure) |
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The Bachelor of Advanced Studies (Honours) (Mathematics (Pure)) requires 48 credit points from this table including: | ||

(i) 6 credit points of 4000-level Honours coursework selective units from List 1, and | ||

(ii) 6 credit points of 4000-level Honours coursework selective units from List 2, and | ||

(iii) 12 credit points of 4000-level and 5000-level 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 | ||

(iv) 24 credit points of 4000-level Honours research project units |

Unit of study |
Credit points |
A: Assumed knowledge P: Prerequisites C: Corequisites N: Prohibition |
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## Honours coursework selective |
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## List 1 |
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MATH4311Algebraic Topology |
6 | A Familiarity with abstract algebra and basic topology, e.g., (MATH2922 or MATH2961 or equivalent), (MATH3961 or equivalent) and (MATH2923 or equivalent) |

MATH4312Commutative Algebra |
6 | A Familiarity with abstract algebra, e.g., MATH2922 or equivalent |

MATH4314Representation Theory |
6 | A Familiarity with abstract algebra, specifically vector space theory and basic group theory, e.g., MATH2922 or MATH2961 or equivalentN MATH3966 |

## List 2 |
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MATH4313Functional Analysis |
6 | A Real Analysis and abstract linear algebra (e.g., MATH2X23 and MATH2X22 or equivalent), and, preferably, knowledge of Metric Spaces |

MATH4315Variational Methods |
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. |

## List 3 |
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4000-level or 5000-level unit from a School other than the School of Mathematics and Statistics. | ||

## List 4 |
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5000-level units from the School of Mathematics and Statistics except STAT5002, STAT5003, DATA5810 or DATA5811. | ||

## List 5 |
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AMSI4001AMSI Summer School |
6 | A Completed a first degree with a major in Mathematics, Statistics, Financial Mathematics and Statistics, Data Science or equivalentThis 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. |

MATH4061Metric 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 |

MATH4062Rings, 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 |

MATH4063Dynamical 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)]N MATH3063 or MATH3963 |

MATH4068Differential Geometry |
6 | A Vector calculus, differential equations and real analysis, for example MATH2X21 and MATH2X23P (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 |

MATH4069Measure Theory and Fourier Analysis |
6 | A (MATH2921 and MATH2922) or MATH2961P (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 |

MATH4071Convex Analysis and Optimal Control |
6 | A MATH2X21 and MATH2X23 and STAT2X11P [A mark of 65 or above in 12cp of (MATH2XXX or STAT2XXX or DATA2X02)] or [12cp of (MATH3XXX or STAT3XXX)]N MATH3971 |

MATH4074Fluid 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 |

MATH4076Computational 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)N MATH3076 or MATH3976 |

MATH4077Lagrangian 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 |

MATH4078PDEs 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 |

MATH4079Complex 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 MATH3068P (A mark of 65 or above in 12cp of MATH2XXX) or (12cp of MATH3XXX)N MATH3979 or MATH3964 |

MATH4411Applied 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 |

MATH4412Advanced 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 |

MATH4413Applied Mathematical Modelling |
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. |

MATH4414Advanced Dynamical Systems |
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. |

MATH4511Arbitrage Pricing in Continuous Time |
6 | A Familiarity with basic probability (eg STAT2X11), with differential equations (eg MATH3X63, MATH3X78), achievement at credit level or above in MATH3XXX or STAT3XXX units or equivalent |

MATH4512Stochastic Analysis |
6 | A Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent |

MATH4513Topics 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 |

STAT4021Stochastic Processes and Applications |
6 | A 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 topicsN STAT3011 or STAT3911 or STAT3021 or STAT3003 or STAT3903 or STAT3005 or STAT3905 or STAT3921 |

STAT4022Linear 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 eigenvectorsN STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904 |

STAT4023Theory 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 statisticsN STAT3013 or STAT3913 or STAT3023 or STAT3923 |

STAT4025Time Series |
6 | P STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933)N STAT3925 |

STAT4026Statistical Consulting |
6 | P At least 12cp from STAT2X11 or STAT2X12 or DATA2X02 or STAT3XXXN STAT3926 |

STAT4027Advanced 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 equivalentP (STAT3X12 or STAT3X22 or STAT4022) and (STAT3X13 or STAT3X23 or STAT4023) |

STAT4028Probability and Mathematical Statistics |
6 | A STAT3X23 or equivalent: that is, a sound working and theoretical knowledge of statistical inferenceN STAT4528 |

STAT4528Probability 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 processesN STAT4028 |

## Honours core research project |
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PMAT4103Pure Mathematics Honours Project A |
6 | |

PMAT4104Pure Mathematics Honours Project B |
6 | C PMAT4103 |

PMAT4105Pure Mathematics Honours Project C |
6 | C PMAT4104 |

PMAT4106Pure Mathematics Honours Project D |
6 | C PMAT4105 and SCIE4999 |

SCIE4999Final Honours Mark |
0 |