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Hello, I’m Brandon,

I am excited to share with you my unique, nontraditional journey and experiences as an avid scholar and professional in mathematics and computer engineering. I am duly eager to share where my passions and experiences have taken me to now, and what lessons from undergrad I feel were most helpful moving forward. I plan to share all of these things with you here in hopes to foster motivation for those planning on pursuing either of these fields, and to hopefully make the journey a little less arduous for others.

I found that I had an admiration for mathematics early on in my course of education, and quickly found my niches in digital logic, set theory of mathematics, and differential equations (ODEs and PDEs). I quickly understood that mathematics such as these, are for individuals willing to push their comprehension of physical nature, and must want to pursue a deeper, foundational understanding of the world around them in terms of mathematics and equations.

During my time in undergrad I collected a slew of diverse and thought-provoking experiences, including: taking a course on epidemiology models, conducting research in AI, learning and utilizing Matlab, and mastering the techniques of Numerical Analysis. Though these experiences are multifarious and quite distinct from one another, they all had an easily overlooked relationship that connected them collaboratively: the finite difference method.

My newfound interest in the finite difference method led me down a rabithole of fervent reading on the subject, where I quickly connected it to my previous understanding in epidemiological models. While I was formulating the code for the finite difference code, I realized that the equations were turned into arithmetic problems and that some of these arithmetic could be replaced by a convolution if the equations were re-arranged. It was rewarding, challenging and fascinating all at once.

I also want to share the obstacles and challenges I am facing as well, the prominent barrier being that I am not trained as an Engineer or Physicist. Since I have spent little time translating physical systems into the differential equations that describe the problem, I do not have the knowledge or practice necessary to formulate the physical interpretations of any of these equations. Thus, I have now met somewhat of a roadblock, and feel unable to move forward with my technique because I don’t know how to implement my work in real world applications.

My next step in this journey is to determine how to conquer this obstacle and move forward. I now find myself questioning what the next best step is. Should I change the trajectory of my career? Move forward in the abstract? Retrain myself as an Engineer? But, which subject do I choose to study then? I continue to find myself feeling confused and unsure of what route is best to take, especially since I still enjoy computer engineering. But, how do I apply this to a simulation format?

I hope that this blog not only provides valuable advice for others, but can also open discussions and commentary around the uncertainty I am facing with my own career and work presently. Additionally, I hope to encourage an environment where students and professionals alike can share what they’ve learned and aid others in finding the most fulfilling and befitting careers in the fields of mathematics, engineering, computer engineering, and/or physics.

I look forward to growing and learning with you!

Best regards, Brandon

Micropost #1 : Arithmetic

💾

Some physical interpretations of arithmetic.
Addition is joining groups, then counting the stars.
Subtraction is removing, then counting the stars.
Division is grouping then counting the number of groups.
Multiplication is making copies, joining them together, 
then counting the stars.

Examples
-----------
1 + 1
[*] join [*]
[**]
One group of two. Count the stars.
count(**)
The answer is 2.

5 + 3
[*****] join [***]
[********]
One group of eight. Count the stars.
Count(********)
The answer is 8.

3-1
[***] remove [*]
[**]
One group of two. Count the stars.
Count(**)
The answer is 2.

6 / 3
[******] group into 3's
[***] , [***]
Two groups of three.
Count the groups.
Just count the groups.
Count( [ ] , [ ] )
Just count the groups!
The answer is 2.

6 / 2
[******] group into 2's
[**] , [**] , [**]
Three groups of two.
Count the groups.
Count( [ ] , [ ] , [ ] )
Just count the groups!
The answer is 3.

2*3
[**] make 3 copies and join them together.
[**] join [**] join [**]
[******]
Three groups of two.
Then one group of six.
Count the stars.
Count(******)
The answer is 6.

Story of My Undergrad: Mathematics & Computer Engineering

When I entered undergrad I quickly was drawn to mathematics, and it wasn’t long until I decided to major in it as well. I learned a variety of subjects, but most of them led up to ODEs, PDEs, and eventually, time-domain PDEs. I found that many of my fellow colleagues learning about ODEs around me commonly asked, “What do I do with this?”. With further observation I concluded that people fell into either of two categories on the subject: those that figured it out, and those that didn’t — it was as simple as that. And those that couldn’t seem to grasp the concept of ODEs seemed to encounter a large impediment, ultimately halting them from being able to learn anything further. But, it became quite apparent that those who successfully figured out ODEs faced their own unique obstacle, thus realizing they knew nothing about the physical nature of the equations they were using in praxis.

Once I felt confident with ODEs I looked to expand my knowledge of mathematics further, broadening my understanding to the computational side of mathematics, which subsequently led to my secondary major in Applied Mathematics. My studies in Applied Mathematics allowed me to acquire a diverse array of new skills, including: taking a course on epidemiological models where I got the chance to see the Z-transform in action, conducting research in AI, experimenting with Matlab, transforming an image into a 3D plot, treating images as maps from the Cartesian plane to monochrome pixel intensities, and exploring image filters in the time and frequency domain. Additionally, my courses in Applied Mathematics touched upon the central idea of Newton and his Deterministic philosophy, which aided in my understanding of the central numerical solution techniques of Numerical Analysis. Each and every one of these experiences provided an important hint to the puzzle: the finite difference method.

Now that I was given a clue to the puzzle, I was set on putting the full picture together. I read ardently into the finite difference method and was able to make new and exciting connections to the concepts I had learned previously in my epidemiological models course. I began to construct code for finite differences, and recognized that the technique turned differential equations into arithmetic problems. I promptly realized that some of the arithmetic could be replaced by a convolution filter if the equations were re-arranged. This discovery opened the doors for me to treat a single pixel in a JPEG image as an initial value, which allowed me to turn the wave equation into an image filter and apply the wave filter to the JPEG. Thus, waves were materialized from the impulse JPEG as a result.

Here is where my own understanding begins to break down. Since I was not trained as either an Engineer or Physicist, I lack the experience and knowledge needed to translate physical systems into the differential equations that describe the problems I have been wrestling with. Thus, I am unable to move forward with my mathematical simulations of the finite difference method because I don’t know how to establish the physical interpretations of any of these equations. Additionally, I am unsure of how to implement this research in real world applications.

Currently, I am examining my options in order to determine what course of action will best help me overcome both the practical and intellectual obstacles hindering me from continuing and concluding my research. The options that I have come up with are to either: quit, move forward with a more abstract research lense, or re-train myself as an engineer. I find myself feeling conflicted, since I still enjoy Mathematics, but lack the skills necessary to apply my research to simulation. Though my career trajectory is still being refined, my goals are to get a job in CFD within the next 2 years and complete a quantitative approach to my studies, consisting of 4 books with 4000 pages total. I hope to find a career path that not only benefits my research, but also fosters my passions and brings me satisfaction and happiness.

Old Career Goals

Data Analyst and Technical Communications Specialist

The Data Analyst and Technical Communications specialist is a unique member of the team who specializes in both data and writing expertise. They typically hold a Bachelor’s or Master’s degree in a quantitative field. Their knowledge of programming, statistics, and writing enables them to investigate questions whose answers depend on data. They communicate high-level technical information between teams who don’t speak the same technical language. They are detail oriented, responsible, and have a knack for understanding complex processes across multiple domains.

Job Titles

Data Analyst, Junior Analyst, Data Scientist, Technical Writer, Technical Editor, Research Assistant, Consultant

Functions

Data Analysts work within Government, Business, or Non-Profit organizations collecting measurements for analysis. Analysts collect measurements from customer databases, sales logs, census data, surveys, scientific experiments, websites, or written field reports. They clean, collate, sort, and store these measurements in database files for efficient storage and retrieval. Once loaded into the database, the measurements, or data, are transferred into statistical analysis software (such as R, Microsoft Excel, Python, or SPSS). Analysts then compute statistics on the data in order to discover underlying patterns and trends within the numbers. These patterns and trends are then written into reports, and passed to managers who use the information as business intelligence.

Technical communications specialists are writers who specializes in effective communication of technical information. Tech. Comm. Specialists write user manuals, help files, copy, reports, and research summaries. They make rhetorical analyses for the document, meaning they

  • Assess the target audience for the document
  • Define the purpose of the document
  • Define the scope of the document
  • Refine the topic of the document

They work hand in hand with analysts, engineers, developers, and experts to gather high-level tech information and translate the jargon to language that members of other departments can understand. Technical communications specialists also generate ideas by brainstorming, plan the content structure of a document, and design the look of the document for visual appeal. They are, in essence, technically trained individuals who also write very well.

Where Analysts are technical experts, often holding a Bachelor’s degree in Computer Science, Mathematics, or any other quantitative research field, but also trained in programming and Statistics, the Technical Communications Specialists are experts in communications, holding the same education but trained in the writing process as well. They work together to break down processes and disseminate information as a team in order to gain a competitive business edge by improving processes and discovering trends in customer behavior.

Keywords

Linux, R, SPSS, Excel, Pivot Tables, Consulting, Research, Writing, Editing, Reports, Business Intelligence, Deep Learning, Artificial Intelligence, Pandas, Python, Tensorflow, Statistical Modeling, Machine Learning

Education Path Options

BS Computer Science , BS Mathematics, BS Physical Sciences → MS Analytics or MBA

BS Computer Science , BS Mathematics, BS Physical Sciences → MS Technical Writing

BS Mathematics → MS Applied Statistics

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