Here is a note on quadratic time lower bound for single-tape Turing Machines. Read section 5.2. It can also be accessed from http://www-cc.cs.uni-sb.de/cct/, go to lecture 5.
Course Description:
This course is a survey of the basic concepts of the theory of
computation, including context-free and context-sensitive languages,
regular sets, finite and pushdown automata, Turing machines,
undecidable problems, complexity with respect to time and space,
NP-completeness, and reducibilities. Prereq: CS 367 and Math 240,
or consent of instructor.