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.

Las Vegas hosted CES 2023. This third and last look at CES 2023 previews upcoming consumer electronics trends that will be crucial for market share.

Definitely start with ICT. Qualcomm CEO Cristiano Amon spoke to CNBC from Las Vegas on China's crackdown and the company's automated driving systems for electric vehicles (EV). The business showed a concept car and its latest Snapdragon processor designs, which offer expanded digital interactions through SalesForce-partnered CRM platforms.

Qualcomm CEO Meets SK Hynix Vice Chairman at CES 2023 On Jan. 6, SK hynix Inc.'s vice chairman and co-CEO Park Jung-ho discussed strengthening www.businesskorea.co.kr.

Electrification is reviving Michigan's automobile industry. Michigan Local News reports that $14 billion in EV and battery manufacturing investments will benefit the state. The report also revealed that the Strategic Outreach and Attraction Reserve (SOAR) fund had generated roughly $1 billion for the state's automotive sector.

Michigan to "dominate" EV battery manufacturing after $2B investment. Michigan spent $2 billion to safeguard www.mlive.com.

Ars Technica is great for technology, society, and the future. After CES 2023, Jonathan M. Gitlin published How many electric car chargers are enough? Read about EV charging network issues and infrastructure spending. Politics aside, rapid technological advances enable EV charging network expansion in American cities and abroad.

New research says US needs 8x more EV chargers by 2030. Electric vehicle skepticism—which is widespread—is fundamentally about infrastructure. arstechnica.com

Finally, the UNEP's The Future of Electric Vehicles and Material Resources: A Foresight Brief. Understanding how lithium-ion batteries will affect EV sales is crucial. Climate change affects EVs in various ways, but electrification and mining trends stand out because more EVs demand more energy-intensive metals and rare earths. Areas & Producers has been publishing my electrification and mining trends articles. Follow me if you wish to write for the publication.

Producers This magazine analyzes medium.com-related corporate, legal, and international news to examine a paradigm shift.

The Weekend Brief (TWB) will routinely cover tech, industrials, and global commodities in global markets, including stock markets. Read more about the future of key areas and critical producers of the global economy in Areas & Producers.

TotalEnergies, Stellantis Form Automotive Cells Company (ACC) A joint-venture to design and build electric vehicles (EVs) was formed in 2020.

Great News about the new Google Business Intelligence Solution

Google has renamed Data Studio to Looker Studio and Looker Studio Pro.

Now, Google releases Looker Studio Pro. Similar to the move from Data Studio to Looker Studio, Looker Studio Pro is basically what Looker was previously, but both solutions will merge. Google says the Pro edition will acquire new enterprise management features, team collaboration capabilities, and SLAs.

In addition to Google's announcements and sales methods, additional features include:

Looker Studio assets can now have organizational ownership. Customers can link Looker Studio to a Google Cloud project and migrate existing assets once. This provides:

• Your users' created Looker Studio assets are all kept in a Google Cloud project.

• When the users who own assets leave your organization, the assets won't be removed.

• Using IAM, you may provide each Looker Studio asset in your company project-level permissions.

• Other Cloud services can access Looker Studio assets that are owned by a Google Cloud project.

Looker Studio Pro clients may now manage report and data source access at scale using team workspaces.

Google announcing these features for the pro version is fascinating. Both products will likely converge, but Google may only release many features in the premium version in the future. Microsoft with Power BI and its free and premium variants already achieves this.

Sources and Further Readings

Google, Release Notes (2022)

Google, Looker (2022)

Effective: August 31, 2022

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Jobs' secret emails became public due to a litigation with Samsung.

Steve Jobs sent Phil Schiller an email at the end of 2010. Top 100 A was the codename for Apple's annual Top 100 executive meetings. The 2011 one was scheduled.

Everything about this gathering is secret, even attendance. The location is hidden, and attendees can't even drive themselves. Instead, buses transport them to a 2-3 day retreat.

Due to a litigation with Samsung, this Top 100 meeting's agenda was made public in 2014. This was a critical milestone in Apple's history, not a Top 100 meeting. Apple had many obstacles in the 2010s to remain a technological leader. Apple made more money with non-PC goods than with its best-selling Macintosh series. This was the last Top 100 gathering Steve Jobs would attend before passing, and he wanted to make sure his messages carried on before handing over his firm to Tim Cook.

In this post, we'll discuss lessons from Jobs' meeting agenda. Two sorts of entrepreneurs can use these tips:

1. Those who manage a team in a business and must ensure that everyone is working toward the same goals, upholding the same principles, and being inspired by the same future.

2. Those who are sole proprietors or independent contractors and who must maintain strict self-discipline in order to stay innovative in their industry and adhere to their own growth strategy.

Here's Steve Jobs's email outlining the annual meeting agenda. It's an 11-part summary of the company's shape and strategy.

Steve Jobs outlines Apple's 2011 strategy, 10/24/10

1. Correct your data

Business leaders must comprehend their company's metrics. Jobs either mentions critical information he already knows or demands slides showing the numbers he wants. These numbers fall under 2 categories:

Metrics for growth and strategy

• As we will see, this was a crucial statistic for Apple since it signaled the beginning of the Post PC era and required them to make significant strategic changes in order to stay ahead of the curve. Post PC products now account for 66% of our revenues.

• Within six months, iPad outsold Mac, another sign of the Post-PC age. As we will see, Jobs thought the iPad would be the next big thing, and item number four on the agenda is one of the most thorough references to the iPad.

• Geographical analysis: Here, Jobs emphasizes China, where the corporation has a slower start than anticipated. China was dominating Apple's sales growth with 16% of revenue one year after this meeting.

Metrics for people & culture

• The individuals that make up a firm are more significant to its success than its headcount or average age. That holds true regardless of size, from a 5-person startup to a Fortune 500 firm. Jobs was aware of this, which is why his suggested agenda begins by emphasizing demographic data.

• Along with the senior advancements in the previous year's requested statistic, it's crucial to demonstrate that if the business is growing, the employees who make it successful must also grow.

2. Recognize the vulnerabilities and strengths of your rivals

Steve Jobs was known for attacking his competition in interviews and in his strategies and roadmaps. This agenda mentions 18 competitors, including:

• Google 7 times

• Android 3 times

• Samsung 2 times

Jobs' agenda email was issued 6 days after Apple's Q4 results call (2010). On the call, Jobs trashed Google and Android. His 5-minute intervention included:

• Google has acknowledged that the present iteration of Android is not tablet-optimized.

• Future Android tablets will not work (Dead On Arrival)

• While Google Play only has 90,000 apps, the Apple App Store has 300,000.

• Android is extremely fragmented and is continuing to do so.

• The App Store for iPad contains over 35,000 applications. The market share of the latest generation of tablets (which debuted in 2011) will be close to nil.

Jobs' aim in blasting the competition on that call was to reassure investors about the upcoming flood of new tablets. Jobs often criticized Google, Samsung, and Microsoft, but he also acknowledged when they did a better job. He was great at detecting his competitors' advantages and devising ways to catch up.

• Jobs doesn't hold back when he says in bullet 1 of his agenda: "We further lock customers into our ecosystem while Google and Microsoft are further along on the technology, but haven't quite figured it out yet tie all of our goods together."

• The plan outlined in bullet point 5 is immediately clear: catch up to Android where we are falling behind (notifications, tethering, and speech), and surpass them (Siri,). It's important to note that Siri frequently let users down and never quite lived up to expectations.

• Regarding MobileMe, see Bullet 6 Jobs admits that when it comes to cloud services like contacts, calendars, and mail, Google is far ahead of Apple.

3. Adapt or perish

Steve Jobs was a visionary businessman. He knew personal computers were the future when he worked on the first Macintosh in the 1980s.

Jobs acknowledged the Post-PC age in his 2010 D8 interview.

Will the tablet replace the laptop, Walt Mossberg questioned Jobs? Jobs' response:

“You know, when we were an agrarian nation, all cars were trucks, because that’s what you needed on the farm. As vehicles started to be used in the urban centers and America started to move into those urban and suburban centers, cars got more popular and innovations like automatic transmission and things that you didn’t care about in a truck as much started to become paramount in cars. And now, maybe 1 out of every 25 vehicles is a truck, where it used to be 100%. PCs are going to be like trucks. They’re still going to be around, still going to have a lot of value, but they’re going to be used by one out of X people.”

Imagine how forward-thinking that was in 2010, especially for the Macintosh creator. You have to be willing to recognize that things were changing and that it was time to start over and focus on the next big thing.

Post-PC is priority number 8 in his 2010 agenda's 2011 Strategy section. Jobs says Apple is the first firm to get here and that Post PC items account about 66% of our income. The iPad outsold the Mac in 6 months, and the Post-PC age means increased mobility (smaller, thinner, lighter). Samsung had just introduced its first tablet, while Apple was working on the iPad 3. (as mentioned in bullet 4).

4. Plan ahead (and different)

Jobs' agenda warns that Apple risks clinging to outmoded paradigms. Clayton Christensen explains in The Innovators Dilemma that huge firms neglect disruptive technologies until they become profitable. Samsung's Galaxy tab, released too late, never caught up to Apple.

Apple faces a similar dilemma with the iPhone, its cash cow for over a decade. It doesn't sell as much because consumers aren't as excited about new iPhone launches and because technology is developing and cell phones may need to be upgraded.

Large companies' established consumer base typically hinders innovation. Clayton Christensen emphasizes that loyal customers from established brands anticipate better versions of current products rather than something altogether fresh and new technologies.

Apple's marketing is smart. Apple's ecosystem is trusted by customers, and its products integrate smoothly. So much so that Apple can afford to be a disruptor by doing something no one has ever done before, something the world's largest corporation shouldn't be the first to try. Apple can test the waters and produce a tremendous innovation tsunami, something few corporations can do.

In March 2011, Jobs appeared at an Apple event. During his address, Steve reminded us about Apple's brand:

“It’s in Apple’s DNA, that technology alone is not enough. That it’s technology married with liberal arts, married with the humanities that yields us the results that make our hearts sink. And nowhere is that more true that in these Post-PC devices.“

More than a decade later, Apple remains one of the most innovative and trailblazing companies in the Post-PC world (industry-disrupting products like Airpods or the Apple Watch came out after that 2011 strategy meeting), and it has reinvented how we use laptops with its M1-powered line of laptops offering unprecedented performance.

A decade after Jobs' death, Apple remains the world's largest firm, and its former CEO had a crucial part in its expansion. If you can do 1% of what Jobs did, you may be 1% as successful.

Not bad.