Notes, summaries, assignments, exams, and problems

Analyzing Algorithm Efficiency

Exponential Recursive Calls

return f(n-1) + f(n-1)

❌ Very bad algorithm
Why: It results in an exponential number of calls and massive recomputation.
Better: Use iterative multiplication or fast exponentiation.

Recursive vs. Iterative Practice

S(n) = S(n-1) + n*n*n

⚠️ Same asymptotic cost as iterative, but worse in practice
Why: Recursion adds significant stack overhead.
Better: Use a loop or a closed-form formula.

Efficient Linear Algorithms

return Q(n-1) + 2*n - 1

✅ Efficient linear algorithm

Multiplications: Θ(n), Additions: Θ(n).
Why: There is no redundant computation.

Optimal Element Inspection

temp = recursive call
if temp <= A[n-1]

✅ Optimal
Why: You must look at every element; therefore, Θ(n) is unavoidable.... Continue reading "Algorithm Efficiency and Summation Reference" »

The Power of Allegory in Animal Farm

I appreciate Animal Farm because it presents complex political ideas in a clear and engaging way. Through the use of animals and a simple farm setting, George Orwell makes the themes of power, manipulation, and inequality easy to understand. I like how the novel functions as an allegory of the Russian Revolution while still feeling relevant to modern societies. The gradual corruption of the pigs is especially effective, as it shows how ideals can be distorted over time. Overall, the book is impactful because it encourages readers to question authority, think critically, and reflect on how power can influence behavior.

Corruption, Propaganda, and Social Control

I like Animal Farm because it presents complex... Continue reading "Animal Farm: Analyzing Power, Corruption, and Allegory" »

Annual Payback Period and Solar Savings

Understanding the financial metrics of solar energy is essential for evaluating its viability. Below are the definitions and examples of the annual payback period and annual solar savings.

1. Annual Payback Period

The annual payback period is the time required to recover the initial investment made in a solar energy system through the savings it generates. It is calculated using the following formula:

Payback Period = Initial Investment Cost / Annual Savings

• A shorter payback period indicates a more cost-effective investment.

Real-Life Example

Suppose a homeowner installs a solar water heater costing ₹50,000. If this system helps save ₹10,000 per year on electricity bills, the payback period is:

50,000 /

ICT in Education

Information and Communication Technology (ICT) is used to enhance teaching and learning processes.

Roles of ICT in Education

• E-learning platforms: Provide online lessons accessible from anywhere.
• Virtual classrooms: Allow real-time interaction through video lessons.
• Digital textbooks and online libraries: Offer easy-to-access electronic materials.

Benefits

• Wider access to learning materials
• Interactive learning
• Supports distance learning

ICT in Medicine

ICT significantly improves healthcare services and patient outcomes.

Roles of ICT in Medicine

• Telemedicine: Enables remote consultations between doctors and patients.
• Electronic patient records: Store patient data digitally for easy retrieval.
• Medical research and data analysis: Support scientific

The Stages of Enlightenment in Plato’s Allegory

Plato’s Allegory of the Cave explains that gaining knowledge is a process that is difficult, painful, disorienting, gradual, and necessary. In the story, prisoners are trapped in a cave where a fire behind them casts shadows on the wall. Because they have never seen anything else, they believe these shadows are reality.

• The Cave: Represents an unexamined life shaped by ignorance.
• The Shadows: Symbolize false beliefs based on misinformation, tradition, and appearances.
• The Fire: Stands for limited sources of knowledge that create these illusions.

When the freed prisoner is released, he is forced to turn around. The firelight hurts his eyes, illustrating why the pursuit of knowledge is difficult

Level 1: Vocabulary and Grammar Practice

Section 1: Key Vocabulary

• 1. Slightly
• 2. Adjust
• 3. Sibling
• 4. Out of the question
• 5. Be focused
• 6. Exhausted

Section 2: Prepositions and Phrasal Verbs

• 1. Under
• 2. Out
• 3. Back
• 4. On
• 5. Over
• 6. In
• 7. Turn

Section 3: Health and Medical Terms

1. Healthcare
2. Prescriptions
3. Meet their expectations
4. Average
5. Assume
6. Prevent

Section 4: Relative Clauses in Sentences

1. The doctor who treated me seemed very young.
2. Nancy, whose leg is broken, won’t be going on the class trip.
3. I can recommend a good spa where you can relax.
4. Pilates, which gives you strength and flexibility, is highly recommended.
5. Doug is following a healthy eating plan that includes fruit and vegetables.
6. I’ll always remember the moment when they told me I was cured.

Section 5: Formal

1. Complete these sentences

• If you get paid badly, you earn too little money.
• A dead-end job offers no opportunities for promotion.
• A stressed worker will probably have mental health problems.
• If you’re out of work, you have lost your job.
• When you plan your work, you accomplish your tasks.
• When a person gets fired, his or her job has come to an end.

2. Correct form of the words in brackets

• I’m sorry, but I don’t feel you’ve got the proper qualifications for this position.
• I need someone reliable. I couldn’t depend on the last few workers.
• They announced her resignation. We’re all going to miss her.
• It’s just seasonal work during the summer months.
• He hopes to work his way up to a managerial position.

3. Complete with the most suitable word

• I’m

Professional Background and Technical Skills

I have always been interested in how technology can be used to improve businesses, especially the decision-making process. I studied Computer Science at university, and through my personal and capstone projects, I realized I enjoy the process of turning messy data into structured information where valid and accurate insights make a meaningful impact.

I also completed an IT co-op where I supported end users of various technical backgrounds, giving me the ability to explain technical concepts to non-technical users in a simple manner—a skill I know would be valuable in this role, mainly when dealing with clients. I am also familiar with Excel, SQL, and Tableau, skills I know would translate well into... Continue reading "Alpha EPM Interview Preparation and Career Strategy" »

Exercise 1: Choose the Correct Answer

Choose the correct answer for each sentence. Only one answer is correct.

1. The train arrives (to arrive) at 12:30. (c)
2. We are having (to have) dinner at a seaside restaurant on Sunday. (d)
3. It is going to snow (to snow) in Brighton tomorrow evening. (a)
4. Paul is flying (to fly) to London on Monday morning. (a)
5. Wait! I will drive (to drive) you to the station. (c)
6. The English lesson starts (to start) at 8:45. (c)
7. I am going to see (to see) my mother in April. (c)
8. Look at the clouds – it is going to rain (to rain) in a few minutes. (a)
9. When they get married in March, they will have been (to be) together for six years. (a)
10. Do you think the teacher will have marked (to mark) our homework by Monday morning? (a)
11. This time

1. Advantages and Disadvantages of Living in the Suburbs

Living in the suburbs is common for many families. The suburbs are usually outside the city center. People choose this lifestyle for different reasons. There are advantages and disadvantages to living in the suburbs.

On the one hand — suburbs are quiet and calm. There is less noise and less pollution. Houses are bigger, and there are more green spaces. It is a good place for families and children.

• Quieter environment: less noise and less pollution.
• Larger homes: houses are typically bigger with more outdoor space.
• More green space: parks and gardens are common.
• Family-friendly: suitable for children and family life.

On the other hand — suburbs are far from the city. People often need a car... Continue reading "Suburbs, Graffiti, and Gentrification: Pros and Cons" »