# Single Honors Mathematics (SF year)
**Source**: https://www.maths.tcd.ie/undergraduate/modules/sf-ubmath-sng.php
**Parent**: https://www.maths.tcd.ie/undergraduate/modules/
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# Single Honors Mathematics (SF year)
**Selected pathway**
Major in Mathematics, Minor in Pillar 1
Major in Mathematics, Minor in Pillar 2
Major in Mathematics, Minor in Pillar 4
Major in Mathematics, Minor in Statistics
Single Honors Mathematics
**ECTS credit split**
## Available pathways
During their Senior Fresh year, students follow one of the available pathways.
Their exact options are depicted in this
[useful diagram](https://www.maths.tcd.ie/undergraduate/modules/Pathways_SH.pdf)
and they are also briefly outlined below.
- **Major with Minor pathway:** Students take 40 credits in Mathematics
modules along with 20 credits in another minor subject.
- **Single Honors pathway:** Students take 40 credits in Mathematics modules
along with 20 credits in Open Modules and Trinity Electives.
Students who follow the former pathway will be able to drop their minor subject
and switch back to the Single Honors pathway a year later, if needed.
## Minor in Statistics or other subjects
To complete a minor degree in another subject, students must take 20 credits in that
subject every year for a total of 60 credits during their studies. One of the available
options is a [minor in Statistics](https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php).
This is designed exclusively for Single Honors Mathematics students and the quota is
high enough to accommodate all students. It is also possible to pursue a minor in various
[other subjects](https://www.tcd.ie/tjh/new-minor-subject).
However, these are offered to several cohorts of students across college and the available
places are limited, so allocations are made based on the candidates' results during their
Junior Fresh year.
## Timetable pillars for minor subjects
For timetable purposes, the available minor subjects (other than Statistics)
are divided into three groups, which are also known as pillars.
- **Pillar 1 subjects:**
Classical civilisation, Drama studies, French, History.
- **Pillar 2 subjects:**
Ancient history and archaeology, Economics, English, Italian, Linguistics, Music.
- **Pillar 4 subjects:**
Classical languages, Geography, Irish, Philosophy, Religion, Social policy, Spanish.
## Open Modules and Trinity Electives
The term [Trinity Electives](https://www.tcd.ie/trinity-electives/electives) refers to a collection of modules on various topics
of general interest including modules in art, history, science and foreign languages, for
instance. These are all modules that have no prerequisites, and the students that do not
pursue a minor must take 1-2 Trinity Electives during their studies.
The term [Open Modules](https://www.tcd.ie/tjh/open-modules)
refers to a collection of modules which are offered by other Schools. These are also modules
of general interest, but some of them may have prerequisites, and some of them are only
available for Mathematics students.
Both Trinity Electives and Open Modules are allocated on a first come first served basis.
## Mathematics modules
The following list of Mathematics modules corresponds to the pathway selected at the
top of this page. One may use the dropdown menu to navigate to other pathways, if needed.
Credits must always be divided equally between the two semesters. Unless indicated
otherwise, each module is worth 5 credits. To view the prerequisites for each module, one
may hover their mouse over the module code. Modules listed with (c) are compulsory.
### Yearlong Mathematics Modules
[MAU22200 (c)](https://www.maths.tcd.ie/undergraduate/modules/MAU22200.php "MAU22200 prerequisites:
MAU11204 Analysis on the real line.")
Advanced analysis (10 ECTS)
[Katrin Wendland](https://www.maths.tcd.ie/people/wendland/)
### Semester 1 Mathematics Modules
[CSU22011](https://teaching.scss.tcd.ie/module/CSU22011 "CSU22011 prerequisites:
Familiarity with Java.")
Algorithms and data structures I
[Vasileios Koutavas](https://www.tcd.ie/scss/people/academic-staff/vkoutav)
[CSU22041](https://teaching.scss.tcd.ie/module/CSU22041 "CSU22041 prerequisites:
MAU11601 Introduction to programming.")
Information management I
[Gaye Stephens](https://www.tcd.ie/scss/people/academic-staff/gstephen)
[MAU22101 (c)](https://www.maths.tcd.ie/undergraduate/modules/MAU22101.php "MAU22101 prerequisites:
None.")
Group theory
[Tommaso Cremaschi](https://www.maths.tcd.ie/people/cremaschi/)
[MAU22203 (c)](https://www.maths.tcd.ie/undergraduate/modules/MAU22203.php "MAU22203 prerequisites:
MAU11100 Linear algebra,
MAU11202 Advanced calculus and
MAU11204 Analysis on the real line.")
Analysis in several real variables
[Adam Keilthy](https://www.maths.tcd.ie/people/akeilthy/)
[MAU22205](https://www.maths.tcd.ie/undergraduate/modules/MAU22205.php "MAU22205 prerequisites:
MAU11100 Linear algebra and
MAU11204 Analysis on the real line.")
Ordinary differential equations
[Miriam Logan](https://www.maths.tcd.ie/people/loganmi/)
[MAU22401](https://www.maths.tcd.ie/undergraduate/modules/MAU22401.php "MAU22401 prerequisites:
MAU11400 Mechanics.")
Advanced classical mechanics I
[Chaolun Wu](https://www.maths.tcd.ie/people/chaolunwu/)
[STU23501](https://teaching.scss.tcd.ie/module/STU23501 "STU23501 prerequisites:
STU12502 Introduction to statistics II.")
Probability and theoretical statistics
[Simon Wilson](https://www.tcd.ie/scss/people/academic-staff/swilson)
### Semester 2 Mathematics Modules
[MAU22102 (c)](https://www.maths.tcd.ie/undergraduate/modules/MAU22102.php "MAU22102 prerequisites:
MAU22101 Group theory.")
Fields, rings and modules
[Sergey Mozgovoy](https://www.maths.tcd.ie/people/mozgovoy/)
[MAU22204 (c)](https://www.maths.tcd.ie/undergraduate/modules/MAU22204.php "MAU22204 prerequisites:
MAU11204 Analysis on the real line OR
MAU22203 Analysis in several real variables.")
Introduction to complex analysis
[Dmitri Zaitsev](https://www.maths.tcd.ie/people/zaitsev/)
[MAU22206](https://www.maths.tcd.ie/undergraduate/modules/MAU22206.php "MAU22206 prerequisites:
MAU22203 Analysis in several real variables.")
Calculus on manifolds
[Florian Naef](https://www.maths.tcd.ie/people/naeff/)
[MAU22402](https://www.maths.tcd.ie/undergraduate/modules/MAU22402.php "MAU22402 prerequisites:
MAU22401 Advanced classical mechanics I.")
Advanced classical mechanics II
[Chaolun Wu](https://www.maths.tcd.ie/people/chaolunwu/)
[MAU22602](https://www.maths.tcd.ie/undergraduate/modules/MAU22602.php "MAU22602 prerequisites:
MAU11202 Advanced calculus.")
Introduction to numerical analysis
[Kirk Soodhalter](https://www.maths.tcd.ie/people/ksoodha/)
[STU22005](https://teaching.scss.tcd.ie/module/STU22005 "STU22005 prerequisites:
STU23501 Probability and theoretical statistics I.")
Applied probability II
[Caroline Brophy](https://www.tcd.ie/scss/people/academic-staff/brophyc1)
### Open Modules and Trinity Electives 2025-26
- [Open Modules (for SF Mathematics students)](https://www.tcd.ie/tjh/assets/pdf/SF-OM-SH-Pathways-Mathematics-25-26.pdf)
- [Trinity Electives (list of options)](https://www.tcd.ie/trinity-electives/assets/docs/trinityelectiveslisting2025-26.pdf)
- [Trinity Electives (further details)](https://www.tcd.ie/trinity-electives/electives)