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

Metallurgical sample preparation for microscopy is a crucial step in analyzing the microstructure and properties of metallic materials. Proper sample preparation is essential to obtain accurate and meaningful results. The process involves several key steps:

1. Sample Selection for Microscopy

Choose a representative portion of the material to be analyzed. Ensure that the sample is free from external contaminants and has a flat surface for preparation.

2. Precision Cutting Techniques

Use a precision cutting method to obtain a small section of the material for analysis. Common cutting techniques include abrasive cutting (using a saw with abrasive blades), wire cutting, or electrical discharge machining (EDM) for hard materials.

3. Sample Mounting for

Bond Characteristics

• Coupon: The interest payment made by the bond issuer, usually expressed as an annual percentage of the bond's face value.
• Par (Face Value): The amount the bondholder receives when the bond matures, typically $1,000.
• Term to Maturity: The time remaining until the bond's maturity date when the issuer must repay the bond's par value.
• Denomination: The face value of the bond, usually in increments of $1,000.
• Quotation: Bonds are quoted as a percentage of their face value (e.g., a bond quoted at 95 is selling for 95% of $1,000, or $950).

Bond Prices, Yield to Maturity (YTM), Current Yield, and Rate of Return (HPR)

• Bond Prices: The market price of a bond depends on interest rates. Prices and interest rates have an inverse relationship.

Discrete Random Variables

Discrete random variables are variables that can take on a finite number of distinct values. In simpler terms, a discrete random variable is a set of possible outcomes that is countable.

Continuous Random Variables

Continuous random variables are random variables that take an infinitely uncountable number of potential values, typically measurable amounts.

Example

1. List the sample space in the given experiment. How many outcomes are possible?

The sample space is: S = {NNN, NND, NDN, NDD, DNN, DND, DDN, DDD}

2. Count the number of defective keyboards in each outcome in the sample space and assign this number to the outcome. For instance, if you list NND, then the number of defective keyboards is 1.

The possible values of X are 0,... Continue reading "Introduction to Statistics: Discrete and Continuous Random Variables, Probability Distributions, and Sampling Techniques" »

Why Reinforcement Learning?

Reinforcement Learning (RL) is important because it enables machines to learn optimal behaviors through interaction with their environment, without needing labeled input/output pairs. It is especially useful in scenarios where the best actions are not immediately known, such as game playing, robotics, or dynamic pricing.

In RL, the agent gradually learns to take actions that maximize cumulative future rewards. Unlike supervised learning, RL focuses on long-term outcomes, rather than just immediate correctness.

Main Elements of Reinforcement Learning

• Agent: The learner or decision-maker.
• Environment: Everything the agent interacts with.
• State (S): The current situation of the environment.
• Action (A): Choices available to

Inventory Fundamentals

One use of inventory is to provide a hedge against inflation. ABC analysis divides an organization's on-hand inventory into three classes based upon annual dollar volume. Cycle counting is a process by which inventory records are verified. The difference(s) between the basic EOQ model and the production order quantity model is that the production order quantity model does not require the assumption of instantaneous delivery. Extra units that are held in inventory to reduce stockouts are called safety stock. Inventory record accuracy would be decreased by increasing stockroom accessibility. The two most important inventory-based questions answered by the typical inventory model are when to place an order and how many of

Introduction: A Data Science Journey

My name is Amit Kadam, and I currently reside in Mumbai. I completed my Bachelor of Engineering (B.E.) degree in 2021. After graduation, the pandemic limited job opportunities, and my family faced financial challenges, so I took my first opportunity at Sterling as a Senior Associate, where I worked for 2.5 years.

Initially, I was responsible for document verification, but I was soon promoted to manage drug health screening processes. In this role, I handled candidate health reports, prepared data for analysis, and developed strong attention to detail and data-handling skills.

During this time, a friend who successfully transitioned into data science encouraged me to explore the field. I started by learning... Continue reading "Data Science Career Transition & Predictive Modeling" »

Question Bank #1 – Net Value Functions

L03 – Engineering Economics & Net Value Applications

Review Questions

Recall the nanoRIMS example discussed in lecture. If the net value of buying the nanoparticles is $0 (the reference), determine the net value per week of having a grad student make the nanoparticles based on the following information:

• Benefit = $896/week
• Cost:
  • Cost of consumable supplies per week: Ingredients & electricity to make one batch as accurately as a grad student does is $5/100 mL * 200 mL/week = $10/week
  • Cost of time: Grad student time is $15/hr * 9 hours/100 mL * 200 mL/week = $270/week
  • Cost of space: Occupying a whole fume hood space for 16 hours during working time is $12.50/hr * 16 hrs/week = $200/week
  • Cost of any device:

What is a Scatter Diagram?

Definition

A scatter diagram (or scatter plot) is a graphical representation of two variables where each point represents an observation consisting of paired values from two datasets. The horizontal axis (X-axis) represents one variable, and the vertical axis (Y-axis) represents the other.

Construction

Each point (x_i, y_i) is plotted on the graph for the corresponding values of the two variables.

Utility in Correlation Analysis

Scatter diagrams are essential for:

• Visualizing relationships: Helps identify if a linear or non-linear relationship exists.
• Direction of correlation:
  • Positive correlation: As X increases, Y increases (points slope upwards).
  • Negative correlation: As X increases, Y decreases (points slope downwards).

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Write an interpretation of r^2 using the template in the Activity 2.1 Readings. We will do this one as a class.

Template: The proportion of the variation in the Y variable that is explained by the SLR model with the X variable is r^2.

For slope : Template: As x var increases by 1 unit, we predict y var  will increase/dec  by ____  y var units.

For y-intercept: When x var = 0 units, we predict that the y var  will be ____ units..

For SLR: Error = epsilon = y - yhat = y - (betahat0 + betahat1x)

SSE = residual1^2 + res. 2^2 +…+ res.  n^2

Standard error of regression = Root MSE (in SAS language)

The text lists six conditions for simple linear... Continue reading "Understanding Simple Linear Regression: R-squared, Slope, and Conditions" »

Key Principles of Financial Budgeting

Entity Principle

Consider the company as a functional entity.

Leadership Principle

The Financial Planning Manager develops and coordinates the budget.

Authority Principle

The Finance Manager supervises and presents the budget to the Board of Directors (Partners).

Participation Principle

Involve all key participants in the budget's preparation.

Commitment Principle

All managers undertake to follow the budget, notifying any deviation in a timely manner.

Goal Principle

The budget is based on the strategic planning objectives.

Accounting Principle

A budget system should mirror the current accounting system.

Measurement Principle

All estimates must be in currency units.

Predictability Principle

The predictions generated must... Continue reading "Financial Budgeting: Principles and Model Development" »