Gallery — Math

I had to relearn LaTeX to turn in my real analysis homework last night, so I made it into a template in case others are in the same situation.

A template for instructors to create exams for Mathematics/Statistics classes.

This is the template for DAM (discrete and argumentative mathematics). We prove theorem $2.1$ using the method of proof by way of contradiction. This theorem states that for any set $A$, that in fact the empty set is a subset of $A$, that is $\emptyset \subset A$.

Created for Stanford Mathematics Camp 2016. A brief introduction to the Hopf Fibration for introductory topology students.

Algebra Linear

MATH 21-127: Concepts of Mathematics Template for homework submission READ THE FOLLOWING CAREFULLY!!! When you produce a PDF version of this document to turn in, change the filename to hwX-name.pdf replacing X with the homework assignment number and name with your last name.

Exercícios

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for ”quotient”. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal). A real number that is not rational is called irrational. Irrational numbers include √2, , e, and . The decimal expansion of an irrational number continues without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost allreal numbers are irrational.

Vibration control is crucially important in ensuring a smooth ride for vehicle passengers. This study sought to design a suspension system for a car such that its mode of vibration would be predominantly bouncing at lower speeds, and primarily pitching at higher speeds. Our study used analytical and numerical methods to choose appropriate springs and dampers for the front and rear suspension. After an initial miscalculation, we succeeded in arriving at appropriate shocks for the vehicle with the desired modes of vibration at the specified frequencies. We then assessed the maximum bouncing and pitching that the vehicle would experience under a specific set of conditions: travel at 40 km/hr over broken, rough terrain. Our testing showed moderate success in our suspension design. We successfully damped the force being transmitted to both the front and rear quarter car somewhat, while ensuring that the modes of vibration fell into the desired shapes at the desired frequency ranges.