I'm a first year student in math Ph.D. program. I'm taking 3 courses (all qualifying exams preparation course) and do TA work about 10 hours a week.
What are some tips for managing my time in grad-school?
a. Start doing homework the day you receive it, not the day before it is due.
b. When you're not sure what to do, study/do math.
Is it better to focus on learning material for one class per day, or allocate a little bit of time each day for each class?
I go for the first approach because I feel it's easier to focus on one of them than to switch back and forth among subjects within a day.
How to grade or teach time efficiently?
a. Before you finish your own exam requirements, choose an easy course to TA (like single variable calculus).
b. Remember unlike you most undergraduate students in lower division courses are not interested in math. They care little except exam/hw scores. Most students who can easily get an A+/A/D/F do not care about you. In discussion section do examples highly related to their HW, Sample Exam, Past Exam and little to nothing else.
c. Set up a good grading rubric that allows you to grade fast. Give full credit to correct answer with some reasonable justifications (even if it's not perfectly written). When it's boarder line give 1 additional point instead of explaining why the answer doesn't deserve an additional point.