New to TeX/LaTeX? After you download and install the below software, peruse The Not So Short Introduction to LaTeX 2e.
If you want a TeX/LaTeX typesetting system for your own personally-owned Microsoft Windows computer like the one used on the UCSD Mathematics Department computers, the application programs you need are:
Q: Why does the department prefer to use the shareware "WinEDT" application rather than one of the free TeX-aware text editors and Windows GUI frontend/IDE shells?
A: The short answer is that it was the best available TeX-aware text editor and Windows GUI frontend/IDE shell at the time we first chose to standardize our computer lab software installation with many years ago and it's what we've always used since. This may change in the future. The long answer is a complicated response which winds up being the same non-ending argument as "vi or emacs?", "Microsoft Word or WordPerfect?", "Mac or PC?", etc.
Q: As a current member of the UCSD Mathematics Department, can I use the department's license of WinEDT on my personally-owned computer?
A: No. Sorry. The department license of WinEDT can only be installed and used on department-owned computers. You must buy your own license of WinEDT for personally-owned computers. Please see the WinEDT Registration webpage for current pricing and license usage restrictions. As of 2014, a WinEDT Personal License for Student use was US $40.00 and a WinEDT Personal License for Educational use (for non-students like faculty/staff) was US $60.00. If WinEDT is still too expensive for your budget, please try out the various free TeX-aware text editors and Windows GUI frontend/IDE shells applications listed above.