You can limit the size by avoiding font inclusion as much as possible and rely on the PDF viewer to supply the fonts, although this practice is discouraged even for the “standard 35” Adobe fonts, nowadays.
Write the file nodownload.map
next to your main document
phvb8r Helvetica-Bold 0 "TeXBase1Encoding ReEncodeFont" <8r.enc
phvb8y Helvetica-Bold 0 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
phvbo8r Helvetica-BoldOblique 64 "TeXBase1Encoding ReEncodeFont" <8r.enc
phvbo8y Helvetica-BoldOblique 64 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
phvr8r Helvetica 0 "TeXBase1Encoding ReEncodeFont" <8r.enc
phvr8y Helvetica 0 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
phvro8r Helvetica-Oblique 64 "TeXBase1Encoding ReEncodeFont" <8r.enc
phvro8y Helvetica-Oblique 64 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
psyr Symbol 3
ptmb8r Times-Bold 2 "TeXBase1Encoding ReEncodeFont" <8r.enc
ptmb8y Times-Bold 2 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
ptmbi8r Times-BoldItalic 66 "TeXBase1Encoding ReEncodeFont" <8r.enc
ptmbi8y Times-BoldItalic 66 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
ptmr8r Times-Roman 2 "TeXBase1Encoding ReEncodeFont" <8r.enc
ptmr8y Times-Roman 2 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
ptmri8r Times-Italic 66 "TeXBase1Encoding ReEncodeFont" <8r.enc
ptmri8y Times-Italic 66 "TeXnANSIEncoding ReEncodeFont" <texnansi.enc
Now compiling the following example
\pdfmapfile{=nodownload.map}
\documentclass[10pt,a4paper,oneside]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathptmx}
\usepackage[scaled]{helvet}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{lipsum}
\title{Test}
\author{John doe}
\begin{document}
\maketitle
\section{This is a test}
\textsf{Abc\itshape def} and an integral
\[
\int_{-\infty}^{\infty}e^{-x^{2}}\,dx=\sqrt{\pi}
\]
\lipsum
\end{document}
produces, for me, a 29 KiB PDF file. To be sure the compression is as high as possible, add the line
\pdfcompresslevel=9
at the beginning, although this shouldn't be necessary.
But 50 KiB for a PDF file is too strict a requirement in any case. I tried pasting the “lipsum” text in a word processor I happen to own (not that one) and print it to a PDF file. Fonts are included even if Times is used.
lmodern
package?Standard Type 1 Fonts (Standard 14 Fonts)
(en.wikipedia.org/wiki/…) (Times. Courier, Helvetica) and forbid embedding them. PDF readers must have 'local' copies of these fonts. Embeded fonts are quite big if you only have 50kb. But this is just as braindead as your instructor.