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• 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
• Theoretical compendium
• Problems
• Number Theory
• Theoretical compendium
• Problems
• Miscellaneous
• Theoretical compendium
• 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