If you're interested in learning more about some of these topics, these resources can help
Nose cone shapes:
Composites:
the book of everything: Composite Materials Handbook
Net Composites - a good terminology reference and a quick read
Advanced Composite Materials - really good introduction/overview; this one's worth reading
Math:
Basic Mechanics of Laminated Composite Plates - if you want to do really detailed composites math
NASA Astronautic Structures Manual Vol 1, Vol 2, Vol 3 - more general structures math and the best astronautic structures handbook
Buckling of Thin-Walled Circular Cylinders - actually really important for building airframes
Testing:
ASTM overview of composites standards - you should skim this one to find the standard you want if you plan to do any testing
Other:
Structural Design Requirements and Factors of Safety for Spaceflight Hardware - it's a good resource for specifics (like how composites might have a higher FoS because they're a little unpredictable) but the summary is that a 1.1 FoS is required for unmanned missions and 1.4 for manned.