Below user Robusto's foregoing answer, user Clément requests sources which I provide here:
I searched this on Google which effected http://www.thestudentroom.co.uk/showthread.php?t=668467&page=2 which then recommended http://www.sussex.ac.uk/informatics/punctuation/capsandabbr/caps:
(c) The names of languages are always written with a capital letter.
Be careful about this; it's a very common mistake.
Juliet speaks English, French, Italian and Portuguese.
I need to work on my Spanish irregular verbs.
Among the major languages of India are Hindi, Gujarati and Tamil.
These days, few students study Latin and Greek.
Note, however, that names of disciplines and school subjects are not
capitalized unless they happen to be the names of languages:
I'm doing A-levels in history, geography and English.
Newton made important contributions to physics and mathematics.
She is studying French literature.
http://www.uottawa.ca/services/lsl/eng/writing-capitalization.html
Subject areas and disciplines
Subject areas like biology, sociology, engineering, women’s studies
and psychology are common nouns and don’t normally take a capital
letter.
- The University of Ottawa has programs in an array of disciplines, from mathematics and medicine to chemistry and criminology.
The same applies to broader areas:
- Professor Doesitall has published extensively in the humanities, pure and applied sciences and arts.
NOTE: Capitalize the first letter in disciplines and subject areas
only:
in an official academic unit title:
- School of Psychology; Department of Theatre, etc.
on a diploma or certificate:
- …so and so has met all of the requirements of the Master’s in Linguistics
and in lists of official degree titles:
- The Department of Social Sciences offers these degrees: Honours Bachelor of Social Science; Master’s in Sociology…
http://www.ucl.ac.uk/prospective-students/pams/audit-design/style-guide
Capitalisation
References to organisations should begin with a lower-case letter unless the title is given in full. For example: ‘The Department of
Mathematics offers several degree programmes. Staff in the department
specialise in...’
Only use initial capitalisation for job roles when singular e.g. ‘Students will be assigned a Personal Tutor. All tutors...’
Academic subjects begin with a lower-case letter unless part of a title. For example: ‘If you are interested in studying mathematics at
UCL, a GCE A level in Mathematics is required.’
http://www.bc.edu/offices/omc/resources/style-guide/capitalization.html
Departments, offices, majors
Academic subjects are lowercase, except when you are describing a
subject that is also a language, culture, or religion.
She is a psychology major and English minor.
He works in the psychology department and the Germanic studies
department.
The formal names of departments, offices, programs, and institutions
should be capitalized; on a second or general/informal reference,
lowercase.
He works in the Department of Psychology.
She works in the Office of Marketing Communications.
You can pick up an application at the admissions office.