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Mechanical Engineer|Extensive experience teaching math & science
Liam F.

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Hourly Rate: $50

About Liam


Bio

I've always believed that the best learning happens when you connect abstract concepts to real-world problem-solving. Throughout my PhD in Mechanical Engineering at Colorado State University, I didn't just study thermodynamics, materials science, and advanced mathematics; I used them daily, applying these principles to design thermal protection systems for hypersonic vehicles and develop novel ceramic materials. This hands-on experience taught me that understanding why equations work is just...

I've always believed that the best learning happens when you connect abstract concepts to real-world problem-solving. Throughout my PhD in Mechanical Engineering at Colorado State University, I didn't just study thermodynamics, materials science, and advanced mathematics; I used them daily, applying these principles to design thermal protection systems for hypersonic vehicles and develop novel ceramic materials. This hands-on experience taught me that understanding why equations work is just as important as knowing how to solve them.

As a Graduate Teaching Fellow, I was selected as the sole representative from the mechanical engineering department to teach and mentor freshman engineering students. What I loved most was watching students' faces light up when a difficult concept finally clicked, that moment when calculus stops being symbols on paper and becomes a tool for understanding the physical world. My approach to tutoring mirrors how I approach a challenging rock climb: break the problem into manageable pieces, identify the critical holds (or concepts), and build confidence through systematic progression. Whether you're struggling with differential equations, need help visualizing free body diagrams, or want to understand the chemistry behind reaction kinetics, I focus on building intuition alongside technical skills.

My academic background includes a BS in Applied Mathematics with a mechanical engineering concentration (3.6 GPA) and a PhD in Mechanical Engineering (3.7 GPA), with coursework spanning linear algebra, thermodynamics, fluid dynamics, materials science, and computational methods. I'm proficient in MATLAB and Python, and I understand how these tools support learning in math and science. Most importantly, I'm patient, enthusiastic, and committed to helping you not just pass your class, but truly understand the material.


Education

University of Colorado Boulder
Applied Mathematics
Colorado State University
PhD

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Approved Subjects

Algebra 1

Algebra 1

Algebra is a subject at the center of my wheelhouse. I've tutored students in Algebra throughout high-school, college, and graduate school. My undergraduate degree is in applied mathematics wherein I used algebra everyday. Even as I taught higher level subjects during graduate school there would always be students who needed extra help with algebra.
Algebra 2

Algebra 2

Algebra is a subject at the center of my wheelhouse. I've tutored students in Algebra throughout high-school, college, and graduate school. My undergraduate degree is in applied mathematics wherein I used algebra everyday. Even as I taught higher level subjects during graduate school there would always be students who needed extra help with algebra.
Calculus

Calculus

I have extensive experience tutoring all levels of Calculus. My first teaching job was an undergraduate student teaching Calculus I and Calculus III. My undergraduate degree is in Applied Mathematics wherein calculus was used on a daily basis. These skills were honed even further throughout my graduate studies in Mechanical Engineering.
Elementary Math

Elementary Math

I have a strong foundation in mathematics with a BS in Applied Mathematics and a PhD in Mechanical Engineering, but what makes me effective with elementary students is my ability to break complex ideas into simple, engaging pieces. As a Graduate Teaching Fellow and mentor, I've learned that building confidence and making math fun are just as important as getting the right answer. I use real-world examples, like measuring ingredients for recipes or understanding patterns in nature, to help young learners see that math isn't just numbers on paper, it's a tool for understanding the world around them. My patient, encouraging approach helps students develop problem-solving skills and genuine curiosity about mathematics.
Geometry

Geometry

I have extensive experience with geometry through my mechanical engineering background, where I've applied geometric principles daily in CAD design, tolerance analysis, and spatial problem-solving. My work with 3D modeling has given me deep intuition for how shapes, angles, and spatial relationships work in both two and three dimensions. I excel at helping students visualize geometric concepts, whether it's understanding proof strategies, calculating areas and volumes, or recognizing how transformations affect shapes, by connecting abstract theorems to tangible examples they can see and touch. My approach emphasizes building geometric intuition alongside technical skills, making even challenging topics like trigonometry and coordinate geometry accessible and engaging.
Mechanical Engineering

Mechanical Engineering

I hold a PhD in Mechanical Engineering from Colorado State University (3.7 GPA) and a BS in Applied Mathematics with mechanical engineering concentration from University of Colorado Boulder (3.6 GPA). My doctoral research focused on advanced materials for aerospace thermal protection systems, where I designed components for hypersonic vehicle leading edges operating in extreme environments exceeding 2000°C. I have extensive hands-on experience in CAD design (SolidWorks CSWA certified, AutoCAD), advanced manufacturing techniques including spark plasma sintering, materials characterization using XRD/SEM/thermal analysis, and comprehensive mechanical testing and instrumentation. I've published peer-reviewed research in Ceramics International, managed externally funded projects, and have six years of experience in mechanical design, thermal analysis, fabrication, and cross-functional project coordination.
Physics

Physics

Physics is central to the engineering classes I've taught for the last 6 years. Every problem in design or analysis boils down to understanding of forces and the reactions they cause. Furthermore, my own work in design of thermal management hardware for hypersonic flight utilizes all sorts of concepts covered in physics classes.
Prealgebra

Prealgebra

Pre-Algebra is where students build the critical foundation for all higher mathematics, and I'm passionate about making sure that foundation is solid. With my BS in Applied Mathematics and years of teaching experience, I know how to break down concepts like variables, equations, and proportions into manageable steps that build confidence. I focus on helping students understand why the rules work, not just memorizing procedures, so they develop genuine problem-solving skills that carry forward into Algebra and beyond. My patient, encouraging approach helps students overcome math anxiety and discover that they're more capable than they thought, turning "I can't do this" into "I've got this!"
Precalculus

Precalculus

Pre-Calculus was the bridge that transformed my understanding of mathematics from procedural to conceptual, and I'm excited to help students make that same journey. With my BS in Applied Mathematics and PhD in Mechanical Engineering, I've used pre-calculus concepts daily, from trigonometry in vector analysis to exponential functions in thermal modeling, giving me deep insight into how these tools connect to real applications. I excel at helping students master the critical topics like functions, trigonometry, conic sections, and limits while building the mathematical maturity needed for calculus success. My approach emphasizes both technical proficiency and conceptual understanding, ensuring students don't just pass pre-calculus but enter calculus with confidence and solid foundations.
Thermodynamics

Thermodynamics

I hold a PhD in Mechanical Engineering from Colorado State University (3.7 GPA) and a BS in Applied Mathematics with mechanical engineering concentration from University of Colorado Boulder (3.6 GPA). My doctoral research focused on advanced materials for aerospace thermal protection systems, where I designed components for hypersonic vehicle leading edges operating in extreme environments exceeding 2000°C. This required extensive application of thermodynamic principles. Additionally, I completed graduate courses in the subject of thermodynamics.
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