Notes, summaries, assignments, exams, and problems for Mathematics

Process Control Elements

Raw Materials Management

Raw materials required for the process must be as specified in the transaction records, with checks on their source, condition, quantity, and production/receipt date. All details should be properly registered.

Labor Force and Training

Every process, regardless of its degree of automation, involves a quantitative and qualitative workforce component, which may be more or less specialized. The workforce employed in a process must be educated and trained in operations. They must be able to distinguish a good product from one that is not, know how to react to non-conformities, and maintain relevant operational records. Personnel can range from trainees requiring strong supervision to highly experienced... Continue reading "Essential Elements of Process Control and Quality Assurance" »

Identification of Financial Statements

The financial statements shall be clearly identified and distinguished from any other information published in the same document.

Characteristics of Financial Statements

• Accuracy: Displaying information in a clear, precise, and true manner.
• Opportunity: Must be submitted on time.
• Relevance: Only present information unique to the company's operations.
• Integrity: The information submitted must be complete and not incomplete or unreliable.
• Frequency: Financial statements should be made with a fixed periodicity.

Notes to Financial Statements

Clarifications or explanations of events or situations, quantifiable or not, are an integral part of every financial statement. They must be read together for correct interpretation.... Continue reading "Financial Statements: Identification, Characteristics, and Inventory Accounting" »

Teaching and Learning Concepts

Concrete Bases (Teaching)

Convert mathematics into something concrete. Create recognizable contexts to which children can assign their own meanings.

Construction (Learning)

Learning is a constructive activity, contrary to the idea that children simply absorb knowledge presented to them.

Models (Teaching)

To achieve progress, students must have tools at their disposal that enable them to establish a link between informal and formal mathematics. Models and materials are important.

Raising the Level (Learning)

The learning process occurs at different levels of formality. Changes can be sudden and create discontinuity in the learning process.

Time for Reflection (Teaching)

The teacher has to find time to include reflection... Continue reading "Principles of Math Teaching and Learning" »

Secondary Data Analysis: Sources and Elaboration

Secondary data analysis considers both qualitative and quantitative perspectives. It uses references like coding sheets in quantitative designs and identifies interviews or focus groups for qualitative data. Official statistics and public sources are used to verify field data.

Desrosieres argues that statistical indicators from official sources reflect social reality in institutions. These indicators are presented without analysis, as tables of results. This means the original data has been elaborated, which is typical of secondary sources. Secondary sources have developed, summarized, and synthesized the data. The degree of elaboration is the key difference between secondary data analysis and... Continue reading "Secondary Data Analysis: Sources, Types, and Elaboration" »

Hurwicz Criterion: Coefficient of Optimism

In this approach, a decision-maker may have an intermediate attitude. Since no probabilities are associated with each state of nature, this author suggests using a coefficient of optimism, simultaneously called C, and a coefficient of pessimism, (1 - C), where 0 ≤ C ≤ 1.

The coefficient C indicates the decision-maker's stance toward risk. When it is closer to 1, the decision-maker will be more optimistic, while closer to 0, the decision-maker is more pessimistic.

This criterion focuses only on the extreme scores of each alternative, weighing the result of maximum optimism with the coefficient C and the result of minimal value with the coefficient of pessimism (1 - C). The sum of these two products... Continue reading "Decision-Making Under Uncertainty: Criteria and Tables" »

Cutting speed depends on mining velocity. The cutter's speed must remain constant throughout its journey through the ore flow.

Sampling Methods

Sampling can be performed using manual or mechanical methods. Manual methods include cone and quartering, sampling with scoops or shovels, and using sampling tubes.

Manual Sampling Techniques

Cone and Quartering

1. Stack material into a conical pile by shoveling.
2. Form a cake or 'qeqe'.
3. Divide the cake into four equal fractions.
4. Take two opposite quarters as the sample; reject the other two.
5. If the sample size is adequate, combine the two retained quarters and reduce their size.
6. Repeat steps 1-4 as necessary until the desired sample size is achieved.

Sampling Scoop or Shovel

This procedure is used when ore is moved... Continue reading "Mining Ore Sampling Techniques and Procedures" »

Fundamental Concepts in Algebra

Numerical Language

Expressing mathematical information using only numbers.

Algebraic Language

Expressing mathematical information using both numbers and letters.

Algebraic Expression

A set of numbers and letters combined with mathematical operation signs.

Numerical Value of an Algebraic Expression

The number obtained by replacing the letters with their corresponding values and performing the indicated operations.

Monomial

A monomial consists of a number and one or more letters:

• The number (including its sign) is called the coefficient.
• The letter or letters that accompany it are called the literal part.

Degree of a Monomial

The sum of the exponents of the letters that form it.

Similar Monomials

Two or more monomials are similar... Continue reading "Fundamental Concepts of Algebra and Equations" »

Fortran 90: Implicit None and Vector Management

Implicit None

In Fortran 90, undeclared variables starting with I, J, K, L, or M are treated as integers, while others are treated as real numbers. However, it's best practice to avoid implicit declarations. Use IMPLICIT NONE right after the program instructions to disable implicit typing. This forces you to explicitly declare all variables, preventing potential errors due to character misuse.

Vector Management Forms

Ordering one-dimensional arrays (vectors) is a common operation. Here are three simple methods: selection, insertion, and bubble sort.

In all cases, we'll assume a one-dimensional array of N elements.

Selection Sort

1. Find the smallest element in the vector.
2. Swap it with the element in the

Joint Cost Allocation Methods

Joint costs are costs of a production process that yields multiple products (co-products). Here's a breakdown of common allocation methods:

Criterion: Market Value

This method allocates joint costs based on the relative sales value of each co-product. Here's how it works:

1. Calculate Total Sales Value:
   • List each co-product (e.g., A, B, C).
   • Determine the sales value per unit (e.g., per kg).
   • Determine the quantity of each co-product produced (e.g., in kg).
   • Multiply the sales value per unit by the quantity to find the total sales value for each co-product.
2. Distribute Total Joint Costs:
   • Calculate the total sales value of all co-products.
   • For each co-product, divide its total sales value by the total sales value of all co-products.