Discrete Mathematics Formulas and Proof Techniques

Posted by on Nov 4, 2025 in Mathematics | 0 comments

Problem: what is the power set P(S) of S=(a,b,c) Solution: ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}.  |p ∨ (p ∧ q) ≡ p|, |p ∧ (p ∨ q) ≡ p|, |p → q ≡ ¬p ∨ q|, |p → q ≡ ¬q → ¬p|, |p ∨ q ≡ ¬p → q|, |p ∧ q ≡ ¬(p → ¬q)|, |¬(p → q) ≡ p ∧ ¬q|, |(p → q) ∧ (p → r) ≡ p → (q ∧ r)|, |(p → r) ∧ (q → r) ≡ (p ∨ q) → r|, |(p → q) ∨ (p → r) ≡ p → (q ∨ r)|, |(p → r) ∨ (q → r) ≡ (p ∧ q) → r|, |p ↔ q ≡

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Essential Physics Formulas: Kinematics and Dynamics

Posted by on Oct 29, 2025 in Mathematics | 0 comments

Cristián Arriagada: Essential Physics Formulas

This compilation provides fundamental equations covering kinematics, dynamics, work, energy, and rotational motion in classical mechanics. These formulas are crucial for solving problems involving motion and forces.

1. Kinematics (Equations of Motion)

1.1. Uniformly Accelerated Motion (MUA)

  • Velocity: V = V0 + a(t – t0)
  • Position: X = X0 + V0t + 1/2 at2
  • Velocity-Position: V2 = V02 + 2a(X – X0)
  • Time: t = (V – V0) / a

1.2. Uniform Rectilinear Motion (MRU)

  • Velocity:
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Understanding 10 Key Principles of Graphic Representation

Posted by on Oct 26, 2025 in Mathematics | 0 comments

Principle of Multiple Application

This patterning process involves the use of a simple figure to represent a variety of objects and body parts. With a limited graphic vocabulary, an artist can represent very different things. This process is useful for its economy of means and communicative effectiveness.

Principle of the Baseline

The baseline is a horizontal line that crosses the drawing near the bottom, serving as the support for characters, animals, plants, and objects. It is a very useful graphical

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Essential Business Math and Financial Formulas

Posted by on Oct 25, 2025 in Mathematics | 0 comments

1. Average Calculation Formula

Formula: Average = (Sum of all values) / (Number of values)

Example: Find the average of 10, 15, 20, 25, 30

  • Sum = 10 + 15 + 20 + 25 + 30 = 100
  • Number of values = 5
  • Average = 100 / 5 = 20

2. Ratio and Proportion Formulas

Ratio: a:b = a/b

Proportion: If a:b = c:d, then a/b = c/d or ad = bc

Example: If 3:4 = x:12, find x

  • 3/4 = x/12
  • 3 × 12 = 4 × x
  • 36 = 4x
  • x = 9

3. Percentage Formulas

Basic Percentage: Percentage = (Part / Whole) × 100

Percentage Increase/Decrease: ((New Value – Old

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Fundamental Numerical Methods and Error Analysis

Posted by on Oct 24, 2025 in Mathematics | 0 comments

1. Error and Its Types

Errors in numerical methods occur due to approximations, limitations in computations, and human mistakes. They can be classified as:

A. Inherent Error

This error naturally exists in the problem itself, independent of numerical methods used to solve it. It arises when the exact value of a quantity is unknown or impossible to determine.

Example:


The value of π\pi is an infinite decimal (3.1415926535…). If we approximate it as 3.14, we introduce an inherent error.

B. Numerical Error

These

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Probability Simulations and Statistical Analysis using R Programming

Posted by on Oct 15, 2025 in Mathematics | 0 comments

 Repeat 1000 times the experiment you performed in Task 1, that is rolling a tetrahedron die 10 times and computing the average. Report the average and standard deviation of the 1000 experiments. The standard deviation function in R is sd(x).

S = 1000
rolls.Avgs = vector(length = S)

for(simnum in 1:S){
  x = 1:4
  roll = sample(x, 10, replace = TRUE)
  rolls.Avgs[simnum] = mean(roll)
}

mean(rolls.Avgs)
sd(rolls.Avgs)

# compute the mean of the 1000 experiments
mean(rolls.Avgs)
hist(rolls.Avgs, main=””, xlab=

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