Wishing for Lasting Companies, Not Penny Stocks or Goodwill Write-Downs

Get me a NASCAR-style company-logoed cremation urn (notice to the executor of my will, theres gonna be a lot of weird requests). I believe in working on projects that would be on your tombstone. As the Homebrew logo is tattooed on my shoulder, expanding the portfolio to my posthumous commemoration is easy. But this isn't an IRR victory lap; it's a hope that the firms we worked for would last beyond my lifetime.

Venture investors too often take credit or distance themselves from startups based on circumstances. Successful companies tell stories of crucial introductions, strategy conversations, and other value. Defeats Even whether our term involves Board service or systematic ethical violations, I'm just a little investment, so there's not much I can do. Since I'm guilty, I'm tossing stones from within the glass home (although we try to own our decisions through the lifecycle).

Post-exit company trajectories are usually unconfounded. Off the cap table, no longer a shareholder (or a diminishing one as you sell off/distribute), eventually leaving the Board. You can cheer for the squad or forget about it, but you've freed the corporation and it's back to portfolio work.

As I look at the downward track of most SPACs and other tarnished IPOs from the last few years, I wonder how I would feel if those were my legacy. Is my job done? Yes. When investing in a business, the odds are against it surviving, let alone thriving and being able to find sunlight. SPAC sponsors, institutional buyers, retail investments. Free trade in an open market is their right. Risking and losing capital is the system working! But

We were lead or co-lead investors in our first three funds, but as additional VCs joined the company, we were pushed down the cap table. Voting your shares rarely matters; supporting the firm when they need it does. Being valuable, consistent, and helping the company improve builds trust with the founders.

I hope every startup we sponsor becomes a successful public company before, during, and after we benefit. My perspective of American capitalism. Well, a stock ticker has a lot of garbage, and I support all types of regulation simplification (in addition to being a person investor in the Long-Term Stock Exchange). Yet being owned by a large group of investors and making actual gains for them is great. Likewise does seeing someone you met when they were just starting out become a public company CEO without losing their voice, leadership, or beliefs.

I'm just thinking about what we can do from the start to realize value from our investments and build companies with bright futures. Maybe seed venture financing shouldn't impact those outcomes, but I'm not comfortable giving up that obligation.

Great technology opens up an universe of possibilities.

Need a friend? WhatsApp, Telegram, Slack, etc.

Traveling? AirBnB, Expedia, Google Flights, etc.

Money transfer? Use digital banking, e-wallet, or crypto applications

Products inspire us. How do we become great?

I asked product managers in my network:

What does it take to be a great product manager?

52 product managers from 40+ prominent IT businesses in Southeast Asia responded passionately. Many of the PMs I've worked with have built fantastic products, from unicorns (Lazada, Tokopedia, Ovo) to incumbents (Google, PayPal, Experian, WarnerMedia) to growing (etaily, Nium, Shipper).

TL;DR:

• Soft talents are more important than hard skills. Technical expertise was hardly ever stressed by product managers, and empathy was mentioned more than ten times. Janani from Xendit expertly recorded the moment. A superb PM must comprehend that their empathy for the feelings of their users must surpass all logic and data.

• Constant attention to the needs of the user. Many people concur that the closer a PM gets to their customer/user, the more likely it is that the conclusion will be better. There were almost 30 references to customers and users. Focusing on customers has the advantage because it is hard to overshoot, as Rajesh from Lazada puts it best.

• Setting priorities is invaluable. Prioritization is essential because there are so many problems that a PM must deal with every day. My favorite quotation on this is from Rakuten user Yee Jie. Viki, A competent product manager extinguishes fires. A good product manager lets things burn and then prioritizes.

This summary isn't enough to capture what excellent PMs claim it requires. Read below!

What qualities make a successful product manager?

Themed quotes are alphabetized by author.

Embrace your user/customer

Aeriel Dela Paz, Rainmaking Venture Architect, ex-GCash Product Head

Great PMs know what customers need even when they don’t say it directly. It’s about reading between the lines and going through the numbers to address that need.

Anders Nordahl, OrkestraSCS's Product Manager

Understanding the vision of your customer is as important as to get the customer to buy your vision

Angel Mendoza, MetaverseGo's Product Head

Most people think that to be a great product manager, you must have technical know-how. It’s textbook and I do think it is helpful to some extent, but for me the secret sauce is EMPATHY — the ability to see and feel things from someone else’s perspective. You can’t create a solution without deeply understanding the problem.

Senior Product Manager, Tokopedia

Focus on delivering value and helping people (consumer as well as colleague) and everything else will follow

Darren Lau, Deloitte Digital's Head of Customer Experience

Start with the users, and work backwards. Don’t have a solution looking for a problem

Darryl Tan, Grab Product Manager

I would say that a great product manager is able to identify the crucial problems to solve through strong user empathy and synthesis of insights

Diego Perdana, Kitalulus Senior Product Manager

I think to be a great product manager you need to be obsessed with customer problems and most important is solve the right problem with the right solution

Senior Product Manager, AirAsia

Lot of common sense + Customer Obsession. The most important role of a Product manager is to bring clarity of a solution. Your product is good if it solves customer problems. Your product is great if it solves an eco-system problem and disrupts the business in a positive way.

Edward Xie, Mastercard Managing Consultant, ex-Shopee Product Manager

Perfect your product, but be prepared to compromise for right users

AVP Product, Shipper

For me, a great product manager need to be rational enough to find the business opportunities while obsessing the customers.

Janani Gopalakrishnan is a senior product manager of a stealth firm.

While as a good PM it’s important to be data-driven, to be a great PM one needs to understand that their empathy for their users’ emotions must exceed all logic and data. Great PMs also make these product discussions thrive within the team by intently listening to all the members thoughts and influence the team’s skin in the game positively.

Director, Product Management, Indeed

Great product managers put their users first. They discover problems that matter most to their users and inspire their team to find creative solutions.

Grab's Senior Product Manager Lakshay Kalra

Product management is all about finding and solving most important user problems

Quipper's Mega Puji Saraswati

First of all, always remember the value of “user first” to solve what user really needs (the main problem) for guidance to arrange the task priority and develop new ideas. Second, ownership. Treat the product as your “2nd baby”, and the team as your “2nd family”. Third, maintain a good communication, both horizontally and vertically. But on top of those, always remember to have a work — life balance, and know exactly the priority in life :)

Senior Product Manager, Prosa.AI Miswanto Miswanto

A great Product Manager is someone who can be the link between customer needs with the readiness and flexibility of the team. So that it can provide, build, and produce a product that is useful and helps the community to carry out their daily activities. And He/She can improve product quality ongoing basis or continuous to help provide solutions for users or our customer.

Lead Product Manager, Tokopedia, Oriza Wahyu Utami

Be a great listener, be curious and be determined. every great product manager have the ability to listen the pain points and understand the problems, they are always curious on the users feedback, and they also very determined to look for the solutions that benefited users and the business.

99 Group CPO Rajesh Sangati

The advantage of focusing on customers: it’s impossible to overshoot

Ray Jang, founder of Scenius, formerly of ByteDance

The difference between good and great product managers is that great product managers are willing to go the unsexy and unglamorous extra mile by rolling up their sleeves and ironing out all minutiae details of the product such that when the user uses the product, they can’t help but say “This was made for me.”

BCG Digital Ventures' Sid Narayanan

Great product managers ensure that what gets built and shipped is at the intersection of what creates value for the customer and for the business that’s building the product…often times, especially in today’s highly liquid funding environment, the unit economics, aka ensuring that what gets shipped creates value for the business and is sustainable, gets overlooked

Stephanie Brownlee, BCG Digital Ventures Product Manager

There is software in the world that does more harm than good to people and society. Great Product Managers build products that solve problems not create problems

Experiment constantly

Delivery Hero's Abhishek Muralidharan

Embracing your failure is the key to become a great Product Manager

DeliveryHero's Anuraag Burman

Product Managers should be thick skinned to deal with criticism and the stomach to take risk and face failures.

DataSpark Product Head Apurva Lawale

Great product managers enjoy the creative process with their team to deliver intuitive user experiences to benefit users.

Dexter Zhuang, Xendit Product Manager

The key to creating winning products is building what customers want as quickly as you can — testing and learning along the way.

PayPal's Jay Ko

To me, great product managers always remain relentlessly curious. They are empathetic leaders and problem solvers that glean customer insights into building impactful products

Home Credit Philippines' Jedd Flores

Great Product Managers are the best dreamers; they think of what can be possible for the customers, for the company and the positive impact that it will have in the industry that they’re part of

Set priorities first, foremost, foremost.

HBO Go Product Manager Akshay Ishwar

Good product managers strive to balance the signal to noise ratio, Great product managers know when to turn the dials for each up exactly

Zuellig Pharma's Guojie Su

Have the courage to say no. Managing egos and request is never easy and rejecting them makes it harder but necessary to deliver the best value for the customers.

Ninja Van's John Prawira

(1) PMs should be able to ruthlessly prioritize. In order to be effective, PMs should anchor their product development process with their north stars (success metrics) and always communicate with a purpose. (2) User-first when validating assumptions. PMs should validate assumptions early and often to manage risk when leading initiatives with a focus on generating the highest impact to solving a particular user pain-point. We can’t expect a product/feature launch to be perfect (there might be bugs or we might not achieve our success metric — which is where iteration comes in), but we should try our best to optimize on user-experience earlier on.

Nium Product Manager Keika Sugiyama

I’d say a great PM holds the ability to balance ruthlessness and empathy at the same time. It’s easier said than done for sure!

ShopBack product manager Li Cai

Great product managers are like great Directors of movies. They do not create great products/movies by themselves. They deliver it by Defining, Prioritising, Energising the team to deliver what customers love.

Quincus' Michael Lim

A great product manager, keeps a pulse on the company’s big picture, identifies key problems, and discerns its rightful prioritization, is able to switch between the macro perspective to micro specifics, and communicates concisely with humility that influences naturally for execution

Mathieu François-Barseghian, SVP, Citi Ventures

“You ship your org chart”. This is Conway’s Law short version (1967!): the fundamental socio-technical driver behind innovation successes (Netflix) and failures (your typical bank). The hype behind micro-services is just another reflection of Conway’s Law

Mastercard's Regional Product Manager Nikhil Moorthy

A great PM should always look to build products which are scalable & viable , always keep the end consumer journey in mind. Keeping things simple & having a MVP based approach helps roll out products faster. One has to test & learn & then accordingly enhance / adapt, these are key to success

Rendy Andi, Tokopedia Product Manager

Articulate a clear vision and the path to get there, Create a process that delivers the best results and Be serious about customers.

Senior Product Manager, DANA Indonesia

Own the problem, not the solution — Great PMs are outstanding problem preventers. Great PMs are discerning about which problems to prevent, which problems to solve, and which problems not to solve

Tat Leong Seah, LionsBot International Senior UX Engineer, ex-ViSenze Product Manager

Prioritize outcomes for your users, not outputs of your system” or more succinctly “be agile in delivering value; not features”

Senior Product Manager, Rakuten Viki

A good product manager puts out fires. A great product manager lets fires burn and prioritize from there

acquire fundamental soft skills

Oracle NetSuite's Astrid April Dominguez

Personally, i believe that it takes grit, empathy, and optimistic mindset to become a great PM

Ovo Lead Product Manager Boy Al Idrus

Contrary to popular beliefs, being a great product manager doesn’t have anything to do with technicals, it sure plays a part but most important weapons are: understanding pain points of users, project management, sympathy in leadership and business critical skills; these 4 aspects would definitely help you to become a great product manager.

PwC Product Manager Eric Koh

Product managers need to be courageous to be successful. Courage is required to dive deep, solving big problems at its root and also to think far and dream big to achieve bold visions for your product

Ninja Van's Product Director

In my opinion the two most important ingredients to become a successful product manager is: 1. Strong critical thinking 2. Strong passion for the work. As product managers, we typically need to solve very complex problems where the answers are often very ambiguous. The work is tough and at times can be really frustrating. The 2 ingredients I mentioned earlier will be critical towards helping you to slowly discover the solution that may become a game changer.

PayPal's Lead Product Manager

A great PM has an eye of a designer, the brain of an engineer and the tongue of a diplomat

Product Manager Irene Chan

A great Product Manager is able to think like a CEO of the company. Visionary with Agile Execution in mind

Isabella Yamin, Rakuten Viki Product Manager

There is no one model of being a great product person but what I’ve observed from people I’ve had the privilege working with is an overflowing passion for the user problem, sprinkled with a knack for data and negotiation

Google product manager Jachin Cheng

Great product managers start with abundant intellectual curiosity and grow into a classic T-shape. Horizontally: generalists who range widely, communicate fluidly and collaborate easily cross-functionally, connect unexpected dots, and have the pulse both internally and externally across users, stakeholders, and ecosystem players. Vertically: deep product craftsmanship comes from connecting relentless user obsession with storytelling, business strategy with detailed features and execution, inspiring leadership with risk mitigation, and applying the most relevant tools to solving the right problems.

Jene Lim, Experian's Product Manager

3 Cs and 3 Rs. Critical thinking , Customer empathy, Creativity. Resourcefulness, Resilience, Results orientation.

Nirenj George, Envision Digital's Security Product Manager

A great product manager is someone who can lead, collaborate and influence different stakeholders around the product vision, and should be able to execute the product strategy based on customer insights, as well as take ownership of the product roadmap to create a greater impact on customers.

Grab's Lead Product Manager

Product Management is a multi-dimensional role that looks very different across each product team so each product manager has different challenges to deal with but what I have found common among great product managers is ability to create leverage through their efforts to drive outsized impacts for their products. This leverage is built using data with intuition, building consensus with stakeholders, empowering their teams and focussed efforts on needle moving work.

NCS Product Manager Umar Masagos

To be a great product manager, one must master both the science and art of Product Management. On one hand, you need have a strong understanding of the tools, metrics and data you need to drive your product. On the other hand, you need an in-depth understanding of your organization, your target market and target users, which is often the more challenging aspect to master.

M1 product manager Wei Jiao Keong

A great product manager is multi-faceted. First, you need to have the ability to see the bigger picture, yet have a keen eye for detail. Secondly, you are empathetic and is able to deliver products with exceptional user experience while being analytical enough to achieve business outcomes. Lastly, you are highly resourceful and independent yet comfortable working cross-functionally.

Yudha Utomo, ex-Senior Product Manager, Tokopedia

A great Product Manager is essentially an effective note-taker. In order to achieve the product goals, It is PM’s job to ensure objective has been clearly conveyed, efforts are assessed, and tasks are properly tracked and managed. PM can do this by having top-notch documentation skills.

Learn or earn

In 2020, I started software engineering. My base wage has progressed as follows:

Amazon (2020): $112,000

Microsoft (2021): $123,000

Google (2022): $169,000

I didn't major in math, but those jumps appear more than a 7% wage increase. Here's a deeper look at the three.

The Three Categories of Compensation

Most software engineering compensation packages at IT organizations follow this format.

Minimum Salary

Base salary is pre-tax income. Most organizations give a base pay. This is paid biweekly, twice monthly, or monthly.

Recruiting Bonus

Sign-On incentives are one-time rewards to new hires. Companies need an incentive to switch. If you leave early, you must pay back the whole cost or a pro-rated amount.

Equity

Equity is complex and requires its own post. A company will promise to give you a certain amount of company stock but when you get it depends on your offer. 25% per year for 4 years, then it's gone.

If a company gives you $100,000 and distributes 25% every year for 4 years, expect $25,000 worth of company stock in your stock brokerage on your 1 year work anniversary.

Performance Bonus

Tech offers may include yearly performance bonuses. Depends on performance and funding. I've only seen 0-20%.

Engineers' overall compensation usually includes:

Base Salary + Sign-On + (Total Equity)/4 + Average Performance Bonus

Amazon: (TC: 150k)

Base Pay System

Amazon pays Seattle employees monthly on the first work day. I'd rather have my money sooner than later, even if it saves processing and pay statements.

The company upped its base pay cap from $160,000 to $350,000 to compete with other tech companies.

Performance Bonus

Amazon has no performance bonus, so you can work as little or as much as you like and get paid the same. Amazon is savvy to avoid promising benefits it can't deliver.

Sign-On Bonus

Amazon gives two two-year sign-up bonuses. First-year workers could receive $20,000 and second-year workers $15,000. It's probably to make up for the company's strange equity structure.

If you leave during the first year, you'll owe the entire money and a prorated amount for the second year bonus.

Equity

Most organizations prefer a 25%, 25%, 25%, 25% equity structure. Amazon takes a different approach with end-heavy equity:

• the first year, 5%

• 15% after one year.

• 20% then every six months

We thought it was constructed this way to keep staff longer.

Microsoft (TC: 185k)

Base Pay System

Microsoft paid biweekly.

Gainful Performance

My offer letter suggested a 0%-20% performance bonus. Everyone will be satisfied with a 10% raise at year's end.

But misleading press where the budget for the bonus is doubled can upset some employees because they won't earn double their expected bonus. Still barely 10% for 2022 average.

Sign-On Bonus

Microsoft's sign-on bonus is a one-time payout. The contract can require 2-year employment. You must negotiate 1 year. It's pro-rated, so that's fair.

Equity

Microsoft is one of those companies that has standard 25% equity structure. Except if you’re a new graduate.

In that case it’ll be

• 25% six months later

• 25% each year following that

New grads will acquire equity in 3.5 years, not 4. I'm guessing it's to keep new grads around longer.

Google (TC: 300k)

Base Pay Structure

Google pays biweekly.

Performance Bonus

Google's offer letter specifies a 15% bonus. It's wonderful there's no cap, but I might still get 0%. A little more than Microsoft’s 10% and a lot more than Amazon’s 0%.

Sign-On Bonus

Google gave a 1-year sign-up incentive. If the contract is only 1 year, I can move without any extra obligations.

Not as fantastic as Amazon's sign-up bonuses, but the remainder of the package might compensate.

Equity

We covered Amazon's tail-heavy compensation structure, so Google's front-heavy equity structure may surprise you.

Annual structure breakdown

• 33% Year 1

• 33% Year 2

• 22% Year 3

• 12% Year 4

The goal is to get them to Google and keep them there.

Final Thoughts

This post hopefully helped you understand the 3 firms' compensation arrangements.

There's always more to discuss, such as refreshers, 401k benefits, and business discounts, but I hope this shows a distinction between these 3 firms.

While our genes can't be changed easily, you can avoid some dementia risk factors. Today we discuss dementia and five drugs that may increase risk.

Memory loss appears to come with age, but we're not talking about forgetfulness. Sometimes losing your car keys isn't an indication of dementia. Dementia impairs the capacity to think, remember, or make judgments. Dementia hinders daily tasks.

Alzheimers is the most common dementia. Dementia is not normal aging, unlike forgetfulness. Aging increases the risk of Alzheimer's and other dementias. A family history of the illness increases your risk, according to the Mayo Clinic (USA).

Given that our genes are difficult to change (I won't get into epigenetics), what are some avoidable dementia risk factors? Certain drugs may cause cognitive deterioration.

Today we look at four drugs that may cause cognitive decline.

Dementia and benzodiazepines

Benzodiazepine sedatives increase brain GABA levels. Example benzodiazepines:

• Diazepam (Valium) (Valium)

• Alprazolam (Xanax) (Xanax)

• Clonazepam (Klonopin) (Klonopin)

Addiction and overdose are benzodiazepine risks. Yes! These medications don't raise dementia risk.

USC study: Benzodiazepines don't increase dementia risk in older adults.

Benzodiazepines can produce short- and long-term amnesia. This memory loss hinders memory formation. Extreme cases can permanently impair learning and memory. Anterograde amnesia is uncommon.

2. Statins and dementia

Statins reduce cholesterol. They prevent a cholesterol-making chemical. Examples:

• Atorvastatin (Lipitor) (Lipitor)

• Fluvastatin (Lescol XL) (Lescol XL)

• Lovastatin (Altoprev) (Altoprev)

• Pitavastatin (Livalo, Zypitamag) (Livalo, Zypitamag)

• Pravastatin (Pravachol) (Pravachol)

• Rosuvastatin (Crestor, Ezallor) (Crestor, Ezallor)

• Simvastatin (Zocor) (Zocor)

This finding is contentious. Harvard's Brigham and Womens Hospital's Dr. Joann Manson says:

“I think that the relationship between statins and cognitive function remains controversial. There’s still not a clear conclusion whether they help to prevent dementia or Alzheimer’s disease, have neutral effects, or increase risk.”

This one's off the dementia list.

3. Dementia and anticholinergic drugs

Anticholinergic drugs treat many conditions, including urine incontinence. Drugs inhibit acetylcholine (a brain chemical that helps send messages between cells). Acetylcholine blockers cause drowsiness, disorientation, and memory loss.

First-generation antihistamines, tricyclic antidepressants, and overactive bladder antimuscarinics are common anticholinergics among the elderly.

Anticholinergic drugs may cause dementia. One study found that taking anticholinergics for three years or more increased the risk of dementia by 1.54 times compared to three months or less. After stopping the medicine, the danger may continue.

4. Drugs for Parkinson's disease and dementia

Cleveland Clinic (USA) on Parkinson's:

Parkinson's disease causes age-related brain degeneration. It causes delayed movements, tremors, and balance issues. Some are inherited, but most are unknown. There are various treatment options, but no cure.

Parkinson's medications can cause memory loss, confusion, delusions, and obsessive behaviors. The drug's effects on dopamine cause these issues.

A 2019 JAMA Internal Medicine study found powerful anticholinergic medications enhance dementia risk.

Those who took anticholinergics had a 1.5 times higher chance of dementia. Individuals taking antidepressants, antipsychotic drugs, anti-Parkinson’s drugs, overactive bladder drugs, and anti-epileptic drugs had the greatest risk of dementia.

Anticholinergic medicines can lessen Parkinson's-related tremors, but they slow cognitive ability. Anticholinergics can cause disorientation and hallucinations in those over 70.

5. Antiepileptic drugs and dementia

The risk of dementia from anti-seizure drugs varies with drugs. Levetiracetam (Keppra) improves Alzheimer's cognition.

One study linked different anti-seizure medications to dementia. Anti-epileptic medicines increased the risk of Alzheimer's disease by 1.15 times in the Finnish sample and 1.3 times in the German population. Depakote, Topamax are drugs.

Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.