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### Pro Tips for Solving Mathematical Problems by O.J.B.:
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### Pro Tips for Solving Mathematical Problems by (O.J.B.):
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| Tip | Explanation/ Details |
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| :--- | :--- |
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| Substitute variables with custom <br> variables (e.g., AbcdEfG) | Solve the equation using your own variables, then mirror the <br> steps onto the original problem for proportional reasoning. |
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| Substitute giveb variables with custom <br> variables (e.g., AbcdEfG) | Solve the equation using your own variables, then mirror the <br> steps onto the original problem for proportional reasoning. |
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| Interpret the equal sign as <br> "converts to" | Thinking of "=" as "converts to" can facilitate substitutions & <br> manipulations in other mathematical expressions. |
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| Think in terms of ratios by <br> default | Viewing values as ratios can simplify problem-solving & <br> conceptual understanding. |
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| Use software tools for conversion <br> to markdown or LaTeX | Convert equations for better inspection & rendering, ensuring <br> accuracy. |
| Solid-State Physics |[Prof. M. S. Dresselhaus](https://web.mit.edu/6.732/www/texts.html)|
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| Transport in Semiconductor Mesoscopic Devices |[David K. Ferry (Book 1)](https://iopscience.iop.org/book/mono/978-0-7503-3139-5) / <br> [David K. Ferry (Book 2)](https://iopscience.iop.org/book/mono/978-0-7503-1103-8)|
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