User:Jlee4203/sandbox

Rationale
STEM is an interdisciplinary approach to education and problem-solving and stands for Science, Technology, Engineering, and Mathematics. This page is dedicated towards exploring how specific STEM fields have led to creative solutions towards everyday problems. The page will explore improvements in efficiency through engineering, unique scientific applications, mathematical research, and technological advancements. Accompanied with observations, this page will provide specific examples in each category that have proven how individuals and their discoveries have led to an improvement in the lives of businesses, economies, and human beings.

The most commonly referred to field in STEM is science. In this current era, regenerative medicine is an emerging field that is deeply rooted in science, that employs bioengineering and molecular biology tools to make advancements in tissue regeneration and repair. Two main subfields that have been introduced in regenerative medicine are STEM cells and 3D organ printing, which in combination, can ultimately change outcomes of lives as they can regenerate tissue that has been affected by diseases. STEM cells have the potential to replace damaged or diseased tissues, and researchers are currently exploring ways to inject them in individuals to treat conditions such as spinal cord injuries and neurological disorders. 3D organ printing, also known as bioprinting, is an innovative technology that fabricates complex three-dimensional structures that mimic the shape and function of natural tissues and organs by layering biomaterials. 3D printing typically involves using computer-aided design software, selecting a specific biomaterial such as polycaprolactone, bioprinting using specialized 3D printers, and transplantation after collecting measurements of the original individual and tailoring size and shape.

The next field in STEM is technology. It is within our current era also known as the fastest growing field. Since the 1960s and 70s, computers’ speed and power have been doubling every one and a half to every two years. 90% of the data we know now was generated in the last two years. Recently, the biggest breakthrough in technology has been advancements in artificial intelligence. Specifically two types of AI: reactive machines and limited memory machines. Reactive machines have no memory and some examples are game bots. Limited memory machines can store data and learn as they receive more data. They work to imitate the neurons in human brains and examples of this is ChatGPT and the technology behind self-driving cars. These technologies have recently been applied to determining whether a cell is cancerous or even whether a newborn has a fatal heart condition called pulmonary hypertension and the degree of the condition from CT scans of the heart. In the case of the cancerous cell, a AI developed in Japan meant for differentiating breads to allow for an easier checkout at bakeries actually turned out to be viable in spotting cancer cells as cancer cells are similar in shape to bread. In the latter example, a group of researchers made a model of an AI that is able to offer input on whether an infant has pulmonary hypertension from its limited memory machine technology. From its learnt datasets, it can apply its knowledge to new scans and determine the chances and severity of the hearts’ condition, in which, a doctor would make the final verdict on whether the infant has the condition saving time and offering treatment as soon as possible.

Another pillar of STEM is Engineering. Engineering seeks to improve systems and their structures using a mix of math, science, computer science and more. Engineers tend to have strong backgrounds in math and science and are apply these skills towards complex problem-solving. There is a certain level of creativity and flexibility also required in engineering. There are no set rules for how to solve world problems, and thus engineers have to draw on a wide range of skills. There is an extremely wide range of possible working fields for engineers. From improving airport routes for maximum efficiency to improving hospital operations to basic business consultation, Engineers must be equipped with the skills necessary to take many potential problems. Engineers are often involved in research, modeling, testing, simulating, data analysis, and more. Engineering is an innately very collaborative field and communication across teams is essential. Many engineers are proficient in coding, graphic design, and modeling. The variety within engineering has often been complimented by those working in its field as it allows for new stimulation within work environments. While some civil engineers can seek out field work and physically watch their engineering projects take shape in real time, other engineers such as industrial engineers can choose to work in an office environment analyzing data and creating reports.

Lastly the least empirical and although also arguably the most fundamental of the four branches STEM is Mathematics. Every other Branch of science uses math at least to some degree. Whether it be a more innately numeric area of science like engineering or physics which are basically just math concepts applied to the real world, or other more nomenclature focused disciplines of science such as biology which still require the aid of certain branches of math like statistics and data analytics to conduct proper well ordered experiments that give meaningful results. It's often the case that some scientific breakthrough can only arise as the practical application of the purely theoretical work of a mathematician. Newton couldn’t have made his majors discoveries in physics if he hadn’t first discovered calculus. How much of today's progress couldn’t have been achieved if the great mathematicians of history hadn’t originally discovered all the formulas scientists needed to crunch the numbers? Humor for a second the idea that everything in biology can be explained through the lens of chemistry, and likewise everything in chemistry can be explained through the lens of physics, and in that manner all the branches of science can be thought to form a single tree. If someone were then to consider it necessary to include math somewhere within the tree, where else could it inevitably go besides at the very root since what other subject could explain all of physics except for mathematics and there on what other discipline from there could possibly hope to explain the infinitely deep well of complexity that is mathematics?

STEM cells
Regeneration is a process that includes inflammation, proliferation, and tissue remodeling through STEM cells and their cytokinines, which can regenerate with self-replication and can be used for treatment of wounds. STEM cells can be divided into totipotent, multipotent, and unipotent STEM cells, and pluripotent STEM cells hve been proven to show significant tissue repair. Currently, the direct application of human embryonic stem cells (ESCs) is being explored with nanopreparations and exosomes, and the combination of these three has emerged in the field of regenerative medicine, an interdisciplinary field that activates STEM cells in the body or implants STEM cells to repair and replace damaged bones and organs in the body. But, many research questions in this field remain unanswered as it is an emerging field and not much is known about STEM cells, and not much is authorized by FDA for experimentation. Therefore, any discovery in this field is considered a breakthrough, and more future research is necessary to provide insight into how STEM cells can improve physiological processes such as tissue regeneration and organ degeneration.

3D organ printing
On March 7 2024, a breakthrough was done in regenerative medicine: a 3D printed organ was successfully transplanted into a patient in Korea at Seoul St Mary’s Hospital. The patient is a woman in her 50’s who lost part of her trachea from thyroid cancer. The 3D printed windpipe is made of a combination of STEM cells, bio-ink, and PCL for structural support that will last up to 5 years. During these 5 years, the transplanted 3D organ will not only serve its purpose as replacing the trachea, but will also promote the body to regenerate the original trachea. 6 months post surgery, the operation was deemed successful as new blood vessels began to form and the windpipe healed properly. The scientists, doctors, and engineers part of this operation collected CT and MRI data to print and transplant the 3D windpipe, with the help of T&R Biofab, a biomedical engineering company. This experiment is one of many to follow that demonstrate the potential of regenerative medicine and practice applications in the field.

National Institutes of Health (NIH) - Regenerative Medicine Program
The purpose of the Regenerative Medicine Program (RMP) at the National Institutes of Health (NIH) is to act as a central hub for stem cell science to quicken the progress of novel medical cell-based applications and therapies. RMP has two initiatives: the SCTL Stem Cell Translation Laboratory (SCTL) as a part of the National Center for Advancing Translational Sciences (NCATS), and a Therapeutic Challenge Award awarded to labs that advance stem cell line research. SCTL and RMP as a whole encourages labs to delve into the emerging and novel regenerative medicine field, such as when the award was given to Dr. Kapil Bharti in 2014 who developed a stem-cell-based therapy to treat macular degeneration, which causes blindness in the elderly. After receiving the award, Dr. Bharti and his research team were motivated to continue research in regenerative medicine and developed an induced pluripotent stem cells (iPSCs) based therapy to prevent blindness, which is a promising tool and is now being further researched.

International Consortium for Regenerative Rehabilitation (ICRR)
The International Symposium on Regenerative Rehabilitation facilitates communication between researchers at different institutions studying regenerative medicine and rehabilitation. There are multiple thematic groups and subdivisions part of ICRR, such as the TERMIS Thematic Group, which brings together researchers from University of Pittsburgh, Kyoto University in Japan, the Mayo Clinic, and the University of Virginia. TERMIS hosts pre-conference workshops, world congress symposiums, and other open public sessions where they collaborate and present regenerative rehabilitation advancements to cultivate a global community that believes in bringing positive change in patient outcomes. Every year, an annual international symposium on regenerative rehabilitation is held- the most recent one was held in Massachusetts on March 7-9 2024. This conference is the largest medical scientific conference for regenerative rehabilitation in the entire world, and is held by world-renowned researchers who are able to present their research and formally and informally network with international attendees during poster sections. The ICRR is supported by the National Institutes of Health under Award Number R13HD085724, and is also supported by multiple renowned organizations who also aim to make breakthroughs in regenerative medicine, such as the National Institute Of Child Health & Human Development (NICHD), the National Institute Of Neurological Disorders And Stroke (NINDS) , the National Institute Of Arthritis And Musculoskeletal And Skin Diseases (NIAMS) , and the National Institute Of Biomedical Imaging And Bioengineering (NIBIB).

What is a STEM cell?
The field of regenerative medicine is often associated with the term “STEM cell”. As regenerative medicine aims to revive and replace damaged tissue in individuals, a major portion of this field’s research revolves around the application of STEM cells or other drug therapies. Essentially, a STEM cell are special human cells that can develop into different cell types and fix damaged tissues. There are two types of STEM cells: embryonic stem cells, and adult stem cells , which has two subtypes: cells from fully developed tissues (brain, skin, bone marrow), and induced pluripotent stem cells (iPSCs), which are modified in the lab to resemble embryonic stem cells. STEM cells can be guided into becoming cells that can regenerate and repair tissues that have been affected by diseases in individuals. Currently, the only stem cell-based products that have been approved by the FDA are blood-forming stem cells (hematopoietic progenitor cells) that are derived from cord blood and can form red blood cells (carry oxygen), platelets (stop bleeding), and white blood cells (fight infections).

What is polycaprolactone?
As mentioned before, regenerative medicine is associated with terms outside of STEM cell, such as polycaprolactone (PCL), a synthetic semi-crystalline biodegradable polyester that can be used for 3D organ printing. On March 7 2024 in Korea, regenerativ medicine was used to create a 3D printed organ (windpipe), which was transplanted into a human using the combination of stem cells and PCL. PCL is a very strong biocompatible, biodegradable, and printable polymer with a low melting point, and research has been done regarding its utility in 3D organ bioprinting for tissue engineering. In 2006, FDA approved 3D-printed PCL scaffolds that can be used for bone fillers in the skull. This procedure has been repeated by many researchers across the world by creating PCL with different structures, such as honeycomb and rectilinear. Thus, PCL can act as structural support and can carry bio-ink (similar to printer ink, but carries living STEM cells that can create living tissue). The only disadvantage of PCL is that as it is biodegradable, it lasts for a maximum of 5 years.

University labs
Internships, shadowing researchers, and joining university labs are the most common ways to engage directly in regenerative medicine. For example, the McDevitt Lab based in California has four initiatives: engineering 3D STEM cell microenvironments, STEM cell molecular therapies, STEM cell analytics and bioprocessing, and engineering micro-scale tissue models. Recently, McDevitt left the lab to join Sana Biotechnology as a Vice President where he will be leading a group to engineer human pluripotent STEM cell technologies, a direct application of regenerative medicine. Andres Garcia, the executive director of the Petit Institute for Bioengineering & Bioscience at Georgia Institute of Technology, is the lead of the Garcia lab which focuses on manipulating biomolecular, cellular, and tissue engineering for direct cell function and application for biomaterial and regenerative medicine. The Temenoff Lab at Georgia Tech is focused on synthesizing and deisnging polymeric biomaterials for orthopedic applications (tendons, ligaments, cartilage, and bone) through biochemical and mechanical stimuli, to promote tissue healing in the field of regenerative medicine. Each of these labs, whether based in Atlanta or across the US, open doors to many possibilities and allow anyone with interest and potential to join the lab to make breakthroughs in the field.

Raising awareness
As regenerative medicine is a new and emerging field, raising awareness is key. A social way to engage in regenerative medicine is to attend public outreach events, seminars, and conferences. Though only FDA-approved labs are allowed to conduct hands-on STEM cell research and 3D organ printing, the general public can attend information sessions to learn more about current research advancements. This will promote them to enter STEM-related career fields and can even help with developing funding resources, as these individuals will gain interest and will want to create fundraisers to promote further research. For example, the Albert Einstein College of Medicine hosts annual STEM cell retreats, which bring together faculty, post-docs, and research graduates from all levels to exchange knowledge. Attending workshops is also another method to engage in regenerative medicine. NIH (including NIAMS) and FNIH host annual 2-day workshops on the future of regenerative medicine which identify activities that can accelerate research, and focus on cellular therapies and the reliability of different materials like PCL.

Same technology behind Pastry AI used to identity cancer cells
BakeryScan, a launched version of pastry A.I. relied on a process developed by Alex Krizhevsky back in 2012. Krizhevsky, who was a graduate student at the time, released a program called AlexNet which utilized a technique called “deep learning” which was efficient in image recognition. Hisashi Kambe, the man behind the pastry A.I. was able to create a program that could differentiate different types of pastries from its appearance. Some bakeries in Japan which employed the use of BakeryScan, would leave a scanner at the register where customers would leave their pastries on the glowing rectangle and then on a separate screen, the prices and names of their pastries would be listed. The use of BakeryScan initially was to help attendants, who normally would have to learn the names of tens or hundreds of pastries and manually enter them at checkout, which compromised sanitation and speed at pastry restaurants. However, later on researchers actually discovered that cancer cells under a microscope looked really similar to bread. With that discovery, BRAIN the corporation behind BakeryScan decided that it could also expand domains with the technology they currently had and formed a new core technology called AI scan. Instead of sugar and bread, AI scans for pathologists could take a slide of a urinary cell and measure the size of its nucleus. And from that AI scan technology, BRAIN currently has a new software called Cyto-AI Scan (which is being used in 2 hospitals in Japan). Cyto-AI Scan does a whole slide analysis and can determine whether a cell is cancerous or not. Of a slide with a number of cells, the AI technology would single out cells that were cancerous based on a score from its visual features and this all started with bread. Translated peer review article: New Yorker

AI detecting birth defects in newborns
Normally, the birth of a baby is accompanied by their first cries. When a newborn takes its first breath, their lungs expand, blood vessels widen, and the circulatory system adjusts to life outside of its mothers’ womb. However, there are newborns who suffer from a condition called pulmonary hypertension where the above process doesn’t occur. Instead, the arteries in the lungs remain narrow so blood can't reach the lungs resulting in less oxygen in the blood as well. Pulmonary hypertension is an extremely serious condition especially for infants who have a more severe variation of the condition, they’d have to be correctly diagnosed and treated as soon as possible for the better of their prognosis. However, detecting the condition is extremely time-consuming and requires a cardiologist with specific expertise and years of experience. Julia Vogt and her team developed a computer model that provides reliable help in diagnosing the condition. The researchers trained the algorithm using images and videos of hearts from 192 infants and had reliable diagnoses for them all by experienced cardiologists: whether pulmonary hypertension was present or not and the degree of its severity. Afterwards, the researchers then had the program determine its own diagnoses on 78 newborn infants (acting as the second dataset) solely based on the knowledge the algorithm acquired from its first analysis. The model had 80-90% correctness in determining whether the condition was present and a 65-85% correct rate in determining the severity of the condition. The program's goal, though, is just meant to be an asset for a human to easily determine whether an infant has pulmonary hypertension and the basis behind its deduction. This technology as stated by Julia Vogt can be used in other medical fields where no specialists are available but a human, a doctor would make the final verdict.

Visual Studio Code
VS Code, short for Visual Studio Code, is a source-code editor released in April 2015 by Microsoft. The editor can be used on Windows, macOS, Linux, and web browsers and operates in 15 languages. The programs’ features include debugging, intelligent code completion, snippets, code refactoring, syntax highlighting, and embedded version control. It also offers extensions which can provide more coding languages, color themes, debuggers and more. The software is free to download and use and with Microsoft Azure individuals can host and deploy React, Angular, Vue, Node, and Python sites directly from VS Code. The programs’ base programming languages include but are not limited to: JavaScript, JSON, Python, Java, Powershell, Markdown, HTML, C++, CSS, TypeScript, PHP, C, C#, YAML, Binary, and GIT Commit Message. The software also allows individuals to use templates to easily start a new coding project. In short, VS Code is a rich text editor (like Atom or Sublime Text) that also has a ton of additional features.

ChatGPT
Developed by OpenAI and Microsoft Corporation, ChatGPT is a free-to-use AI system with over 100 million users and was released in November 2022. ChatGPT is a sibling model to InstructGPT and stands for Chat Generative Pre-Trained Transformer. The model is trained to follow prompts and provide swift and direct responses. ChatGPT can be used for conversations, gain insights, complete tasks, and the growth of AI. A new update to ChatGPT allows users to use their voices to engage in conversation with the AI. ChatGPT was trained via Reinforcement Learning from Human Feedback (RLHF). AI trainers use fine-tuning and play both sides - the user and the AI assistant. From that dialogue dataset, the AI is able to learn and transform its own dialogue format. There is also a reward model involved, where two or more model responses are ranked by AI trainers and tuned using a Proximal Policy Optimization. From this process, many series are differentiated. ChatGPT is adapted from the GPT-3.5.

Artificial Intelligence
Artificial intelligence also known as machine intelligence is, as its name suggests, is intelligence demonstrated by machines or artificial beings (robots for example, in contrast to natural intelligence which are humans or animals). It can also be seen as a simulation of human intelligence by machines in the form of computer systems. Artificial intelligence can be applied in a number of ways: natural language processing, speech recognition, machine vision, and expert systems. There are 4 main types of AI: reactive machines, limited memory machines, theory of mind, and self-awareness. Reactive machines have no memory and are task specific, an input would return the same output. Limited memory machines have an algorithm that imitates the way our brains’ neurons work. It uses deep learning and gets smarter as it receives/learns more information. Theory of mind and self-aware AI are theoretical types. Theory of mind has the potential to understand the world and other entities’ thoughts and emotions. Self-aware AI would be the development of AI that has a conscious understanding of its existence or known as its “sense of self”.

Encryption
Encryption is a process of encoding typically important information in cryptography. Cryptography is the process of someone or something hiding or coding information so that only the intended user can uncover/read the information. This process is still used nowadays in bank cards, ecommerce, and computer passwords. Encryption is turning the plaintext - or original regular of the information - and converts it into a new hidden version called ciphertext. Ciphertext is a transformed version of plainview text by an algorithm and you can turn the ciphertext back into plaintext through decryption. Encryption usually uses a key, this key is hidden from people that the message was not directed to, and only with this specific key can one decode the message and uncover the original plaintext. Modern versions of encryption used in examples listed above are secure because computers cannot actually crack the encryption which is why passwords are safe unless intentionally leaked.

Take beginner computer science courses
One way you can participate in technology in STEM, is by taking beginner coding or computer science courses. Some examples of these courses are offered by large corporations such as Google or by higher institutions (universities). The program at Google, is an entry-level IT support course that awards participants that complete the course with a certificate that proves their knowledge afterwards. The certificate can be shareable on LinkedIn and in general is an industry certification. Skills individuals are expected to learn are customer service, network protocols, cloud computing, encryption algorithms, and debugging. There are also computer science boot camps offered by universities such as one offered by Chapel Hill, or at Emory. These boot camps offer live online classes and allow for students to better network. Not only that, these courses are also typically free and publicly available for individuals that want to learn something new or are simply interested in a career in computer science (without actually having to go to college for the degree).

Offer expertise on online platforms/teaching groups
If you are an individual with prior coding or computer science experience, instead of offering time or money to engage in the discipline you can offer your expertise. You can create your own teaching groups either within your community or online to underprivileged children who cannot normally choose to do so themselves. Platforms like Udemy, Coursera, and Teachable will allow individuals with expertise to create and publish their own courses. These are existing platforms already that have a high number of visitors. Or you can directly contribute to a platform by becoming an instructor or creating content. Such platforms such as Coursera, edX, or Codecademy offer those services. Individuals can also host workshops or webinars within the realm of your expertise. You can promote the event on local billboards or event charts for children or even adults who are also interested in getting involved. If you so choose to do so, you can also work periodically in freelance teaching services like tutoring on your own time and with a group or individual basis.

Reducing Hospital Wait Times
Engineering ultimately seeks to improve efficiency of systems. The purpose is to create new ideas through machinery, tools, or changes in environment. One example of this is a team working with Singapore General Hospital in 2018 that implemented engineering to reduce hospital wait times. The purpose of reducing wait times was to hopefully increase patient satisfaction, decrease unnecessary loads on doctors, and decrease overall patient mortality. By providing an initial analysis of the wait time to consultation, engineers were first able to identify the causes behind long wait times. A lack of manpower, space limitations, a lack of tracking, absence of feedback and more issues were the cause behind longer wait times. After recognition of the issue, the team was able to devise and eventually help the hospital to implement a plan to reduce the wait times. The engineers designed a board to help doctors keep real time visibility of work distribution. The engineers also adjusted the roster for patients to reduce congestion and open up more time to be devoted towards high-risk cases. Finally, the team also recognized a common practice for junior doctors to seek the opinions of senior-doctors during the late stages of patient care instead of the beginning. By implementing a team based model of work, the doctors allowed for communication to be constant so that care plans could be implemented without deviation. The study overall saw a success with a 38 minute decrease in wait time, showing the potential for engineers to create solutions that have real world impact.

Improving Airport Efficiency Through Reduced Winter Maintenance
A group of engineers studied how to optimize the winter maintenance of Kosice airport in Slovakia and consequently lowering the negative environmental impacts of aviation. By reducing the amount of time spent towards winter maintenance, the group sought to save time, and make the operations of the airport more efficient. The team was able to create equations to predict how much time cleaning movement areas of the airport would take using input variables such as snow height and intensity, machinery performance, surfaces, already cleaned parts, and more. The team was able to provide estimations for available departure and arrival times at the airport. The algorithm developed by the team was able to take into account runways, taxiways, and connecting routes. Although the study itself was not put into practice, this study shows how engineers are able to create efficient simulations for testing. The optimization of time allows aircrafts to spend less time in the air waiting for clear runways and consequently reducing unnecessary pollutants and emissions.

Microsoft Power BI
Microsoft Power BI is a useful presentation tool for those working with data. Expansive spreadsheets are often difficult to explain and gather simple conclusions from. Power BI is able to transform the results of data into visual creations. The program itself is easily shared through other platforms such as Teams, PowerPoint, and Excel. The program itself is not exclusive to engineers. Many can use Power BI as a way to visualize future business trajectories and easily share models with potential clients, team members, and employees. Power BI has proved itself useful for analytics, data scientists, and  IT specialists. A unique service provided through Power BI is its use of AI to create visual insights. The ability for Power BI to automatically create graphics has a quality impact on communication in fields with high complexity.

Microsoft Access
Microsoft Access is another tool useful in highly data-driven fields. Access is useful for storing and analyzing large amounts of data or other forms of information. Access allows users to more easily organize project information. Access is also adaptable for different projects and businesses through its customizable options. Similarly to Power BI, Access is also able to be integrated with other Microsoft Products. Users have complimented the ability to collaborate through access feasibly. Access also assures customers of their program's security. Business administrators using Access for sensitive information such as yearly revenues, salaries, and budgets can control this information and track user's activities to assure safety.

Deviation in Engineering
Deviation in general is when someone or something strays from an expected path. In a context more related to the engineering project seeking to reduce hospital wait times, deviation can indicate instances where valuable resources such as time are used towards non critical tasks. As a result of deviations, the attentions of the hospital staff were not directed to patients as appropriately as they may have been. Reducing instances of these deviations maintains a base level of efficiency within the realm of hospital patient processing. Optimal efficiency within the hospital system subsequently led to reduced patient fatality and lower stress on doctors. Notably, deviation within engineering does not always lead to negative outcomes. Deviation can also indicate a necessary change in initial planning that leads to a better outcome in processing.

Algorithms for Modeling
Algorithm Modeling is a tool used in engineering to simulate or predict the efficiency of a system. Physical models are used by engineers for many purposes such as structural modeling like bridges. Optimizing models can be used to improve efficiency such as lowering costs. More applications of algorithms include machine learning and Artificial Intelligence systems that can be used to predict outcomes and make decisions given data. Algorithms are a crucial tool in engineering and mathematics.

Research Opportunities
Engaging in research opportunities is both a way in which people can become more educated about various engineering disciples as well as contribute to open source data. Through various research internships or co-ops, those with interests in engineering can grow their knowledge from base level to more hands on experience. Certain platforms will allow engineers to share their work globally so that others can grow their experience as well. One example of these platforms is GitHub, where users are able to share their software and code through a collaborative working environment. Encouraging the growth and sharing of knowledge in this field through more specific involvement raises the quality of engineers worldwide. This allows for growth in many dimensions of engineering as each engineering discipline is related to each other. Different fields dip into the knowledge of other engineering disciplines to yield the best outcomes for separate yet related projects.

Engineering Committees
Serving on engineering committees is an opportunity to contribute to engineering practices. Individuals can also attend forums to share knowledge and promote a collaborative environment rather than a competitive one. These forums and committees can help to create standards and encourage the exchange of ideas. Individuals can also share their own priorities and address their concerns within specialized fields, shedding light on areas that some engineers may not have been previously exposed to. Teamwork in engineering societies sparks new ideas and also helps move technology forward faster, making engineering easier globally. Some of the first societies for engineers, such as the Boston Society of Civil Engineers established in 1848, serves as a connecting point for civil engineers to focus on supporting the field of civil engineering through training, programs, and other initiatives. Many other societies exist to support their own fields and improve collaboration.

Black-Scholes Equation
$$C = N(d_1)S_t - N(d_2)Ke^{-rt}$$


 * C = call option price
 * N(d) = probability of price going down
 * St = spot price
 * Kt = strike price
 * t = time till maturity
 * r = risk free rate of interest

The Black-Scholes equation is the mathematical foundation for the Black-Scholes investment model, a highly influential derivative investment model widely used in the pricing of European style call options. Both the equation and the model were first published by Fischer Black and Myron Scholes in their 1973 paper The Pricing of Options and Corporate Liabilities which eventually ended up winning them the 1997 Nobel Peace Prize in economics. The basic idea of a call option is that for a fee you can purchase the "option" from a stock seller to buy the stock at a later date at it's current price. If the stock price goes up you cash in on the "option" by buying the stock at the original price, and then turning around and selling it for a profit. If the stock goes down you don't cash in, meaning at most you only lost the fee you paid for the option. The cost of the fee is called the call option price, the original price of the stock is called the spot price, and the future price of the stock is called the strike price. The point of the Black-Scholes equation is to determine what the fair price of a call option should be so that the buyer and seller are just as likely to make a profit. The goal of the Black-Scholes model then is to solve the equation using methods of differential equations to come up with a final price. The model works by first assuming the price of a given stock is subject to a form of Brownian motion meaning that at any given point in time the price will randomly increase or decrease some amount under normal distribution. It then takes into account the general trend of the stock and joins it with the stocks volatility to estimate the the final price.

SVD
$$M = U\Sigma V^{T} $$ SVD stands for single value decomposition which is an advanced technique in Linear algebra used to factorize any matrix into a rotation matrix, a scaling matrix, then another rotation matrix. The idea of a SVD is a generalization of polar decomposition another common concept in linear algebra that only works for real square matrices. Because of the lack of restrictions SVDs possess, they act as a versatile tool for solving many problems often encountered in linear algebra. For one SVDs can be used to solve least squares regression problems, where given a set of random data points it might be advantage for someone to want and find the line of best fit which SVDs can help with. As well SVDs can often be helpful when trying describing an ellipse. A well know practical use of Singular Value decomposition outside of just mathematics is in the field of digital image processing. In computer science the values that coincide with the pixels that make a digital image are commonly stored as numbers contained in matrices. But if each pixel requires at minimum eight bytes and more commonly twenty four bytes just to represent one color value that can rack up a lot of data usage very quickly. But if the image doesn't need to be super detailed, what breaking that matrix of pixels into an SVD allows is for a computer to create a compressed approximation of the original image that's a lot easier to store and transfer.

Desmos
Desmos is the world's most popular free advanced online graphing calculator. It is ran and up kept by Desmos Studio which is a "Public Benefit Corporation with a goal of helping everyone learn math, love math, and grow with math". Meant to assist people of all skill levels the layout of the calculator is designed to be concise and user friendly while also offering advanced features for the more knowledgeable. The main draw of Desmos for most users, which makes it preferred over other online graphing calculators is its seamless UI and its impressive ability to smoothly draw just about any function. No only does it include standard polynomial, logarithmic, and exponential functions but also more advanced and obscure stuff like the erf function and the gamma function.

In addition Desmos studio also offers other math tools on their website such as, a basic four function calculator, a scientific calculator, a matrix calculator, a geometry tool, and a recently released 3D calculator. As well Demos studio has partnered with numerous of the leading online learning resources as well as institutions in charge of "the majority of U.S. state-level assessments and digital college entrance exams"

Wolfram Alpha
Wolfram Alpha is a free online user prompt answering engine focused mainly on mathematics which has been active since 2009. Wolfram's mission statement is to "collect and curate all objective data; implement every known model, method and algorithm; and make it possible to compute whatever can be computed about anything". The program goes a step further than a regular search engine by running user inputs through sophisticated ai algorithms designed to interpret natural language and then systematically implementing the result through an extensive library of expert curated math solving techniques.

Although the program is most well known for its ability to procedurally generate answers to difficult math problems the engine is also capable of pulling from their extensive library of trusted sources to answer questions on a broad range of subjects from biology and chemistry to people and economics. In the past large companies such as Bing and Amazon Alexa have partnered with Wolfram alpha to power their search engines capabilities to solve user generated math questions.

Gaussian Integral
$$\int\limits_{-\infty}^{\infty} e^{-x^2}dx = \sqrt\pi$$

The gaussian integral is a non elementary function that was first published in the early 19th century by the prolific mathematician Carl Friedrich Gauss and is often hailed as one of the most important and widely applicable results in mathematics due to its relation to probability and normal distribution. The gaussian integral is defined as the improper integral from bounds negative infinity to infinity of the gaussian function which has the base form of $$e^{-x^2} $$. When graphed the gaussian function makes a bell shaped curve extending across the natural number line. More specifically with some scaling it graphs a normal curve, of which the area underneath can be understood to represent relativistic probability between two point on the x axis. $$\ prob(x_1,x_2) =\int\limits_{x_1}^{x_2}{e^{-{1\over 2}({x-\mu\over \sigma})^{2}}\over {\sigma\sqrt{2\pi}}}dx $$


 * $$\mu$$ = mean
 * $$\sigma$$ = standard deviation
 * $$x_2$$ = upper bound
 * $$x_1$$ = lower bound

As an example of how this might actually be used, imagine someone were to take a census of the heights of all the undergraduate students attending Georgia Tech. Say they were to find the average height to be about 5,10  with a standard deviation of 3 inches and that the results roughly adhere to normal distribution. So if we wanted to find the approximate percentage of all students that are 6 feet tall or shorter we use the following equation.

$$prob = \int\limits_{-\infty}^{72}{e^{-({{x-70}\over4})^2/2}\over{4\sqrt{2\pi}}}dx \approx 0.691 $$

Which would indicate about 69% of the total student body are 6 feet tell or shorter. Unsurprisingly this and similar equations tend to show up quite often not only in statistics and data science but also in many other fields that deal with probability. Economists use gaussian integrals to describe the inherent randomness associated with the price of stocks in popular hedge funding strategies such as the Black-Scholes model. Physicists use gaussian integrals in quantum physics to describe probability fields used to model probability fields of quarks and photons. Really in just about any academic discipline one could probably find some example of a gaussian integral being use to describe a probability distribution, its that powerful and widespread.

Fourier Transformation
The [https://byjus.com/maths/fourier-transform/#:~:text=Fourier%20Transform%20is%20a%20mathematical,%2C%20RADAR%2C%20and%20so%20on. Fourier transformation] is an advanced method of approximation that allows one to decompose functions under certain parameters into just the sum of multiples of sine and cosine waves. It was first discovered by French mathematician Joseph Fourier in the early 19th century during his study of heat transfer as a method to solve the heat equation. Since then it has become ingrained as an important mathematical concept used extensively in the fields of real and complex analysis as well many other more specialized branches of mathematics. In addition the Fourier transformation has found many practical applications over the years outside of the bounds of pure mathematics. Briefly mentioned before upon its first conception the Fourier transformation was first used as a way a to solve the heat equation which is the basis of how modern physicists and engineers numerically model the diffusion of thermal energy over time across one or more objects. As well because of their ability to breaks down complex frequencies into simpler ones, Fourier transformations are commonly used in anything having to do with audio or signals. For example modern noise suppression technology works by first breaking down a sound using a Fourier transformation into sine waves and then removing terms of corresponding frequencies.

Math Minor
A good option for people who may be interested in math enough to maybe want to pursue it academically could be to consider adding a math minor to their degree. Taking rigorous upper level math courses in order to go for a math minor is a great way to boost a person’s mathematical skills. In addition, a math minor can often act as a good supplement, both in the field and on a resume, for a lot of majors that are considered adjacent to math such as business, data analytics, physics, engineering, computer science, and a whole score of others. In the case of physics and computer science majors specifically, it's not uncommon to see a lot of those students also go for a math minor or even yet dual major in math. This is partly due to the importance of math in those fields but also because students in those fields tend to end up taking a lot of the classes needed for a math minor because of their major anyways. By pursuing a math minor, a person not only gains a firm underlying understanding of general mathematical knowledge but also ends up further developing other important skills such as critical thinking, logical reasoning, and general problem solving abilities that are useful in any field of work as well as being heavily valued by employers.

Math Stack Exchange
A generally good, low commitment way for people to engage further with math is to browse the online mathematics stack exchange. Stack exchange is a popular online Q&A platform for people to come ask questions and share collective knowledge related to different fields of knowledge. The platform is broken up into a large web of separated forums sites each focusing on a different academic discipline. Some popular stack exchange sites include Stack overflow for programmers, English Stack exchange for linguists, etymologists, and English majors and of course the Mathematics stack exchange for all people interested in learning math. Anyone free to ask questions on these websites whether it's for help on a homework problem or out of a curious desire know more about certain topic. The goal of the math stack exchange in particular is to act as a "Q&A for people studying math at any level and professionals in related fields" Within the site one can find a wealth of knowledge on all things math related, whether it be something as elementary as basic algebra or something as far advanced as complex analysis or even better yet, up to date information on progress currently being made in the modern fringe fields of contemporary mathematics.