S(n).
This lecture on Geometric Analysis is about group actions on geometric objects. There are loads of comprehensible introductions: for a web-based account similar to the present lecture notes cf.
D. Bump. For a pretty long list of books on the subject cf.
Zlibrary, in particular:
Groups and Symmetries by Yvette Kosmann-Schwarzbach. A bunch of videos, e.g. a historic account:
N.J. Wildberger: Simple Groups, Lie Groups and the search for symmetries I and
II or a brief intro:
Representation Theory I,
Representation Theory II
The domains for the Z-library online books have been seized. May be the library is still available via the Tor network! Also have a look at PDFDrive.
For your homework you are free to choose documents, but I insist on using the main lectures notations. Do not try to introduce new concepts; you just have to deliver veritable
summaries of three sections of the course. Keep your homework as simple as possible and don't explain any result by a more obscure result.
Be it that you've got a valid user&password combination you may choose the subject (i.e. sections of the main coures) of your homework and you may upload both your homework and your solutions to exams. When choosing these sections please keep in mind that I don't appreciate selecting consecutive sections! The exams involve occasionally heavy matrix manipulations. Hence you are advised to use a computer algebra system of your choice (cf. e.g.
wikipedia) or maybe
ChatGPT. However, if a solution to those examples is provided at all, it will be a series of
maxima or
sage commands. Cf. in particular
Sage for Linear Algebra or
A First Course in Linear Algebra. For the latter program it's advisable (though not required) to know some basics in
python (cf. also
python tutorial. You may also look at
gap, which is a system for computational discrete algebra with particular emphasis on computational group theory. I won't advocate for non open software!
The file name of any uploaded solution to an exercise must start with your name (family name only, case doesn't matter) immediately followed by the number of the exam - this number only serves as a provisional lable and it may change in the future, anyway simply take its present value! As for your homework there are no naming rules. All uploaded files need to be of type: application/pdf and they must be produced by some typesetting software, cf. the sample file:
tmp1.pdf. Please avoid uploading any handwritten stuff! Alternatively I would like to encourage you to use a very basic combination of
MathJax and
LaTeX - I'd opt for this mode, for it's much easier to carry out corrections and in addition the files are way smaller. Actually you only need to know one thing about MathJax: any text delimited by single or double dollar signs is going to be interpreted by MathJax as a LaTeX expression. If you decide for the latter method just take the SOURCE of the sample file
tmp1.html as template change it accordingly (only change the content and 'text' attribute of the 'div' container of class 'exer' and the content of the subsequent 'p' container, don't touch any other part!) rename the file as explained above and
uplaod the resulting html-file. To get the SOURCE use the option 'Page Source' (hopefully provided by your browser) while viewing the page
tmp1.html. Do not download the displayed page, for that gives you just a bunch of MathJax code, which must be purged anyway! Alternatively just copy/paste the contents of the files
template_en.txt or
template_de.txt. If you need assistance in html & css have a look at
w3school,
internetingishard or write an
email. Some final remarks: 1. Try to solve the exams by means of results (theorems, propositions, lemmata, exams, etc.) presented during the lecture. 2. Somtimes your solution to an exam of conceptual nature could be a bit laborious; in that case a solution in line with the lecture will be provided.
The
provisional grading key for the lecture is based on the number of uploaded exams (50%) and on the evaluation of your homeworks (50%). Less than two uploaded exams per semester amounts to: insufficient, two or three: sufficient, four or five: satisfactory, six or seven: good, more than seven: excellent. Once an exam is uploaded a further upload of the same exam only counts fully if the solution differs considerably! Also notice that some of the examples count twice: they are colored navy:
Exam whereas ordinary exams are colored blue:
Exam. This is a program in progress and therefore the arrangement of the results as well as the enumeration of the exams may float slightly, so please always include the description of the exam and not merely its number and its solution. Anyway, try to keep up to date!
The
provisional grading key for any other course (EX/PS/SE) depends on a weighted mixture of assessments of your homeworks by me (66%) and
participating students (33%), sufficient turnout provided!
If you think that these notes are flawless - well, that is just an error on your part!
Feel free to
report any shortcomings, flaws, etc. General
info,
email and
uplaod of exams, homeworks, notes, etc.