Undergraduate amth problems

Undergraduate Math Problems Júlia Turró Comas

O bjectives
Learn new mathematic techniques
Solve problems of a certain difficulty
Try to find more than one solution

Structure
Geometry
Theoretical compendium
Problems
Algebra
Problems
Number Theory
Problems
Miscellaneous
Problems

Geometry
Relation between angles, sides and area of plane triangles
Pythagoras' theorem
Thales theorem. Similarity of triangles
Apollonius’ theorem
Ptolemy’s theorem
Angles in a circumference
Trigonometric functions of multiples angles and other relations
Golden ratio
Outstanding points of a triangle
Power of a point with respect to a circumference

Problem 1
A right circular cone has base of radius 1 and height 3. A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube?

Algebra
Fundamental theorem of Algebra
Cardano-Vieta formulas
Maximum and minimum of derivable functions
Binomial formula
Polynomial remainder theorem
Homogeneous systems

Problem 2
Show that the following system has no real solution.

Number theory
Fermat’s little theorem
Congruence relation
Geometric series

Miscellaneous
Pigeonhole principle
Principle of mathematical induction
Integer part

Conclusions
Acquisition of new mathematic concepts
Discovered mathematics' ambiguity
Gained knowledge in English
Unknown mathematics’ world

Undergraduate amth problems

by Júlia Comas on Feb 14, 2010

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