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  1. Alright, future engineers!
    **Normal Distribution:** A common, bell-shaped probability distribution where data clusters around the mean.
    Ex: Human heights, test scores. Mean = Median = Mode at the center!
    Pro-Tip: Crucial for modeling & predicting real-world outcomes.
    #Stats #Probability #STEM #StudyNotes

  2. Alright, future engineers!
    **Cartesian Product:** A set of all possible ordered pairs where the first element is from the first set & the second from the second.
    Ex: A={1,2}, B={a,b} -> AxB = {(1,a), (1,b), (2,a), (2,b)}
    Pro-Tip: `|AxB| = |A| * |B|`. Essential for combining domains!
    #SetTheory #DiscreteMath #STEM #StudyNotes

  3. Alright, future engineers!
    **Cartesian Product:** A set of all possible ordered pairs where the first element is from the first set & the second from the second.
    Ex: A={1,2}, B={a,b} -> AxB = {(1,a), (1,b), (2,a), (2,b)}
    Pro-Tip: `|AxB| = |A| * |B|`. Essential for combining domains!
    #SetTheory #DiscreteMath #STEM #StudyNotes

  4. Alright, future engineers!
    **Kinetic Energy (KE):** Energy an object has due to its motion.
    Ex: `KE = 0.5 * m * v^2`. A moving car has KE.
    Pro-Tip: It's a scalar value & always positive! Direction doesn't matter, only speed.
    #Physics #Energy #STEM #StudyNotes

  5. Alright, future engineers!
    **Kinetic Energy (KE):** Energy an object has due to its motion.
    Ex: `KE = 0.5 * m * v^2`. A moving car has KE.
    Pro-Tip: It's a scalar value & always positive! Direction doesn't matter, only speed.
    #Physics #Energy #STEM #StudyNotes

  6. Maxwell's Cradle II Kit
    Maxwell's Cradle II is A desktop toy that shows the power of magnetism. A steel ball runs on a slightly curved acrylic track, being given a small "kick" by the electromagnetic coil in the center.
    extkits.co.uk/maxwells-cradle-
    #kits #makers #stem #science

  7. Maxwell's Cradle II Kit
    Maxwell's Cradle II is A desktop toy that shows the power of magnetism. A steel ball runs on a slightly curved acrylic track, being given a small "kick" by the electromagnetic coil in the center.
    extkits.co.uk/maxwells-cradle-
    #kits #makers #stem #science

  8. Alright, future engineers!
    **Modulo Arithmetic:** The remainder when an integer is divided by another.
    Ex: `17 mod 5 = 2` (17 / 5 leaves 2).
    Pro-Tip: Think clock arithmetic! Crucial for cryptography, hashing, and cyclic systems.
    #DiscreteMath #NumberTheory #STEM #StudyNotes

  9. Styrofoam has spent decades acting immortal. Now fungi acting like a real fun guy - edits the ending. Waiting for the biomemetic answer for carbon capture. sciencealert.com/gut-fungi-fro #STEM #scifi

  10. Styrofoam has spent decades acting immortal. Now fungi acting like a real fun guy - edits the ending. Waiting for the biomemetic answer for carbon capture. sciencealert.com/gut-fungi-fro #STEM #scifi

  11. Alright, future engineers!
    **Derivative:** The instantaneous rate of change of a function. It's the slope of the tangent line at any point.
    Ex: Power Rule: `d/dx(x^n) = n*x^(n-1)`
    Pro-Tip: It's your go-to tool for finding max/min values (optimization)!
    #Calculus #Derivatives #STEM #StudyNotes

  12. Alright, future engineers!
    **Dot Product:** A scalar value measuring how much two vectors point in the same direction.
    Ex: For `u=[1,2], v=[3,4] -> u.v = (1*3)+(2*4)=11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

  13. Alright, future engineers!
    **Dot Product:** A scalar value measuring how much two vectors point in the same direction.
    Ex: For `u=[1,2], v=[3,4] -> u.v = (1*3)+(2*4)=11`.
    Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)!
    #LinearAlgebra #VectorMath #STEM #StudyNotes

  14. Alright, future engineers!

    **Standard Deviation (SD):** Measures how spread out data points are from the mean. Ex: Test scores avg 75. SD=5 means most scores are near 75. SD=15 means scores vary widely. Pro-Tip: A small SD indicates data consistency/precision!
    #Stats #DataAnalysis #STEM #StudyNotes

  15. Alright, future engineers!
    **Logarithms:** The inverse of exponentiation. They tell you what power a base needs to become a specific number.
    Ex: `log_b(x) = y` is equivalent to `b^y = x`. So `log_2(8)=3` means `2^3=8`.
    Pro-Tip: Use them to solve for variables *stuck in exponents*!
    #Algebra #MathTips #STEM #StudyNotes

  16. Alright, future engineers!
    **Logarithms:** The inverse of exponentiation. They tell you what power a base needs to become a specific number.
    Ex: `log_b(x) = y` is equivalent to `b^y = x`. So `log_2(8)=3` means `2^3=8`.
    Pro-Tip: Use them to solve for variables *stuck in exponents*!
    #Algebra #MathTips #STEM #StudyNotes

  17. Alright, future engineers!
    **Graph:** A set of nodes (vertices) linked by connections (edges).
    Ex: Friends in a social network are nodes, friendships are edges.
    Pro-Tip: Use graphs to model relationships & find optimal paths/flows.
    #GraphTheory #DiscreteMath #STEM #StudyNotes

  18. Alright, future engineers!
    **Power Set:** The set of all possible subsets of a given set.
    Ex: For A={1,2}, P(A) = {{}, {1}, {2}, {1,2}}.
    Pro-Tip: If a set has 'n' elements, its power set will always have 2^n elements. Count 'em!
    #SetTheory #DiscreteMath #STEM #StudyNotes

  19. Alright, future engineers!
    **Power Set:** The set of all possible subsets of a given set.
    Ex: For A={1,2}, P(A) = {{}, {1}, {2}, {1,2}}.
    Pro-Tip: If a set has 'n' elements, its power set will always have 2^n elements. Count 'em!
    #SetTheory #DiscreteMath #STEM #StudyNotes

  20. It's SciAnts News Friday! Join us as we discuss the cool science news of the week! New species, dolphin tools, bee counting, glyco-RNA, and more!

    9pm EDT

    #science #twitch #TwitchPartner #live #stem #sciants #livestream #scicomm #twitchambassador

    twitch.tv/sciants_Stre...

  21. It's SciAnts News Friday! Join us as we discuss the cool science news of the week! New species, dolphin tools, bee counting, glyco-RNA, and more!

    9pm EDT

    #science #twitch #TwitchPartner #live #stem #sciants #livestream #scicomm #twitchambassador

    twitch.tv/sciants_Stre...

  22. Alright, future engineers!
    **Trapezoidal Rule:** Approximates definite integrals by summing areas of trapezoids under the curve.
    Ex: For `y=f(x)`, area over `[a,b]` is `~ (b-a)/2 * (f(a)+f(b))`.
    Pro-Tip: Use more trapezoids (smaller `h`) for better accuracy!
    #NumericalIntegration #CalcHacks #STEM #StudyNotes

  23. Alright, future engineers!
    **Interleaving:** Mixing different problem types or topics in one study session.
    Ex: Study Ch 1 Calc, then Ch 3 Physics, then Ch 2 Diff Eq.
    Pro-Tip: Boosts problem-solving flexibility by forcing your brain to discriminate strategies!
    #StudySmart #BrainHacks #STEM #StudyNotes

  24. Alright, future engineers!
    **Spaced Repetition:** Reviewing material at increasing intervals to move info to long-term memory.
    Ex: Study a topic today, then in 3 days, 7 days, 14 days.
    Pro-Tip: Use flashcard apps (Anki!) to automate your personalized review schedule!
    #StudySmart #MemoryHacks #STEM #StudyNotes

  25. AI designs viruses that work in a lab - still no idea what our 7-11 hot dogs are made of. bbc.com/news/articles/c5y3j3ng #STEM #scifi

  26. AI designs viruses that work in a lab - still no idea what our 7-11 hot dogs are made of. bbc.com/news/articles/c5y3j3ng #STEM #scifi

  27. Alright, future engineers!
    **Work (W):** Energy transferred when a force causes displacement.
    Ex: `W = F * d * cos(theta)`. Pushing a box.
    Pro-Tip: Only the force component *parallel* to the displacement does work! Perpendicular forces do none.
    #Mechanics #EnergyTransfer #STEM #StudyNotes

  28. Alright, future engineers!
    **Determinant:** A single scalar value derived from a square matrix.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: If `det = 0`, the matrix is NOT invertible (no unique solution for systems!).
    #LinearAlgebra #MatrixTips #STEM #StudyNotes

  29. Alright, future engineers!
    **Determinant:** A single scalar value derived from a square matrix.
    Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
    Pro-Tip: If `det = 0`, the matrix is NOT invertible (no unique solution for systems!).
    #LinearAlgebra #MatrixTips #STEM #StudyNotes

  30. Alright, future engineers!
    **Newton's Third Law:** For every action, there is an equal & opposite reaction force.
    Ex: You push a wall, the wall pushes back on you.
    Pro-Tip: These forces act on *different* objects, never on the same one! #Physics #N3L #STEM #StudyNotes

  31. 🧑‍🤝‍🧑 People who feel content in their friendships are more likely to report better physical and mental health

    ✨Follow the link for more information on this story✨
    scimex.org/newsfeed/your-good-

    #science #sciencenews #research #stem #facts #knowledge #sciencefacts #friends #mentalhealthawareness

  32. 🐈 This week's #ExpertSpotlight is Adelaide Uni's Dr Julia Henning

    🐕 Julia is an animal welfare researcher with specialties in animal behaviour and their emotions🐶😺

    More here: scimex.org/experts?name=julia-

    #science #sciencenews #research #stem #facts #knowledge #sciencefacts