Notes following this MIT course and is based on the xv6 toy operating system. Operating System Interfaces Processes and Memory Forking Exec Operating System Organization Abstracting Physical Resources CPU Modes Processes xv6 startup Security Page Tables Kernel Address space Xv86 Implementation Physical Memory Allocation Xv86 Physical Memory Implementation Process Address Space Sbrk (Xv86) Exec (Xv86) Real World Paging Operating System Interfaces Operating systems serve a number of purposes Abstracts away lower level hardware, so that programs don’t have to care about what disk you are writing to Allows multiple programs to run “at the same time” Provide well defined interface for programs to interact with each other For the interface, we want a simple interface that is easy to implement, but allows high sophisticated operations to happen UNIX philosophy of composing many simple programs together helps keep this problem trackable Can divide operating system into kernel space and user space kernel space is the program which provides services to other programs....

Linear Regression You have a set of data $(x_{i},y_{i},\sigma_[i])$, where x is the independent variable, y is the dependent variable, and $\sigma$ is the uncertainty in the dependent variable You want to fit a line to the data ($\hat{y} = mx+b$) You also want the uncertainties of the parameters Why would you want to do this? To know the parameters of the model To extrapolate/interpolate values of the dataset that you don’t have How you do this depends on your viewpoint a frequentist approach would try to maximize the likelihood estimate (information theory) Suppose that you have a probability density for the data $y_{i}$ ranging from 1 to N Treat this density as a function of the parameters....

Logistics Book(s) Landau and Lifshitz Kardar Pathria Thermodynamics 0th Law Thermodynamic equilibrium means that each object in thermal contact with each other have the same temperature Ideal gases, as you cool them down, all converge to a single point, which defines absolute zero. For Kelvin,, the triple point of water defines the size of each step on the scale (273.16 K) 1st Law $dE = \delta W + \delta Q$ The change is energy can either come from work, or heat $dE = E_{f}-E_{i}$ Energy is a function of state (path independent) $\delta W$ and $\delta Q$ are path dependent Can expand out $\delta W$ into more parts: $dE = -p dV + \delta Q$, where the negative sign comes from the fact that the system does work on the outside environment You don’t need to be restricted to pressure and volume....

IEEE Floating Point Standard Arrays Numerics Random Numbers LCM (Linear Congruent Method) Testing RNG Nonuniform Distributions Non-Analytic Nonuniform Distributions Interpolation Linear Interpolation Fitting Basis Coefficients Polynomial fits Fourier Basis Integration Trapezoid Rule Simpson’s Rule Rescaling Integrals Differentiation Scaling Linear Algebra LU SVD Eigensystems Uses Principal Component Analysis (PCA) Dimensional Reduction Root-Finding Minimization Quadratic Fit Golden Section Search Multi-Dimensional FFTs ODEs PDEs Initial Condition Problems Boundary Condition Problems MCMC (Markov Chain Monte Carlo) Markov Chain Metropolis Hastings Burn-in and Proposal Distribution IEEE Floating Point Standard $\pm 1+ 2^{e-127}\Sigma_{i=0}^{22} f_{i} 2^{-(i-23)}$ e is the exponent number $f_{i}$ represents the floating bits Some edge cases: e = 0, $f \neq 0$ are called subnormal numbers, where “1” above is replaced with 0 and $e-127$ is replaced by $e-126$ e=0 and f=0 is a signed zero e=255, f=0 is a signed $\inf$ e=255, $f\neq = 0$ is NaN Arrays TL;DR if you want to go fast, then use numpy arrays, since they are more contiguous in memory (and hence cache friendly) compared to python lists You also don’t have to worry about type checking since Python needs to check if operations There are also some built-in functions that numpy provides which are faster than Python built-ins Numerics TL;DR Keep numbers from being too small and too large and you’re good $E[\delta (f(a))^{2}] \approx E[[\frac{\partial f}{\partial a}]^{2} \delta a^{2}]$ Assuming similar errors for each operations, you find that the round-off error scales as $\sqrt{N}$ Making finer time steps yields a better approximation, but the round-off error degrades this....

Taken from Experimental Techniques in Modern High-Energy Physics: by Hanagaki, Tanaka, Tomoto, Yamazaki Why? Two basic categories of HEP experiments Find any new particle by converting collision energy to particles Done through finding resonances in the final state Investigate the nature of a particular interaction Done through precise measurements of other physical observables In theory, you work with a small number of states to keep problems tractable. Experimentally, you can get thousands of final states which you have to parse through The number of particles goes as $ln \sqrt{s}$ where s is the square of the center of mass energy of the collision This the angular density to go up, which create “jets” (ie....

Notes adapted from MIT Digital Electronics Lab Also from here Boolean Algebra Theorems Truth Tables Specific Functions 1-Bit Functions 2-bit Functions XOR Overview Verilog Basics Variables Parameters Operators and Loops Enums Syntax Oddities Combinational Logic Continuous Assignment Procedural Assignment Glitches! Gotchas Nesting Modules Combinational Versus Sequential Logic Latches Characteristic Equations Registers Verilog for Sequential Blocks Sequential Always Blocking and Non-Blocking Assignment External Signals (Metastability) FSMs FSM State Encoding Converting to Verilog Clocks PLLS The Treachery of Clocks Skew Jitter Proper usage Timing Timing Parameters Slack Video Black and White TV Color TV VGA HDMI Memory History of Memory Key parameters of memory FPGA SRAM Fabric Case Studies Off FPGA Memory EPROM Family DRAM Buffering DRAM FSM Modularization Pipelining Math Complexity Division CORDIC AXI AXI Signals Signed Number DSP48 CRCs Polynomial Arithmetic Boolean Algebra Theorems Let all variables be boolean in nature (ie....

Notes taken while reading “The Art of Electronics”. I realized that my electronics knowledge is a bit spotty and more theoretically inclined, hence why I’m doing this. The Basics, Because You Have to Start Somewhere Resistors Resistor Rule’s of Thumb Voltage Dividers Thevenin Equivalence Misc Use Cases Capacitors Common Applications RC Time Constants Frequency Filters Differentiators Integrators Inductors Applications Voltage Converters Transformers Diodes Applications Rectifiers Dual Rail Power Supply Voltage Multipliers Biasing Logic Gates Clamps Limiters Logarithm Inductive Kickback Transistors (BJTs) BJTs (Bipolar Junction Transistors) Transistor Switches and Saturation Switching From High Pulse Generator Schmitt Trigger Impedences of Sources and Loads Emitter Follower Emitter Follower Biasing Case Study Canceling Offset Transistor Current Sources Common-emitter Amplifier Unity Gain Phase Splitter Phase Shifter Transconductance Ebers-Moll equation Rules of thumb Emitter Follower Redux Bias Stability Current Mirrors The Basics, Because You Have to Start Somewhere There are two quantities that we care about with circuits: Voltage and Current...

Logistics Principle of “Least” Action Symmetries Gauge Invariance Example Reduce to Quadratures Hamiltonian Mechanics Phase Portraits Poisson Brackets Properties Jacobi Proof Sketch Poisson’s theorem Canonical Transformations Why We Care Liouville’s Theorem Canonical Invariants Entropy Tangent Infinitesimal CTs Hamiltonian Noether’s Theorem Hamilton Jacobi Equation Action Variables Multiperiodic motion Planetary motion Liouville’s Integrability Theorem Cannonical Peturbation Theory Adiabatic Motion Quantum Mach Zender Hilbert Space Linear Algebra Review Time Evolution Heisenberg Formulation Compatible Observables Symmetries Uncertainty Relationship Phase Space Interpretation Entanglement And Mixed States Mixed States Von Neumann Entropy Partial Trace (“Tracing Out”) Infinite Spaces Translation Operator Scattering Probability Current Delta Function Path Integral Free Particle Saddle Point Approximation Path Integral Proof WKB Logistics Matthew Klebon klebon@nyu....

An introduction to databases. Logistics Intro Data Models Database Design Phases Bad Design ER Model Drawing ER Diagrams SQL (Structed Query Language) SQL Schema SQL Query Anatomy SELECT and FROM WHERE AS keyword String Operations LIKE ORDER BY Set Operations UNION INTERSECT EXPECT Null Values Aggregation GROUP BY HAVING Nested Subqueries Subquery tests for WHERE Subquery test for FROM DELETE, INSERT, UPDATE DELETE INSERT UPDATE JOINS Natural/Inner Joins Outer Joins Views Integrity Constraints Authorization Privileges Roles Object-relational Databases Complex Types User Defined Types Inheritance Textual Data Big Data Streaming Data Physical Storage Types Interfaces Magnetic Disks Flash RAID RAID Levels Indexing Ordered Indices B+ Tree Hash Indices Transactions Scheduling Query Processing Parsing Optimization Evaluation Relational Algebra Building Execution graph Query Cost Relational Algebra Implementations Selection Sorting Joins Duplicate elimination Projection Set Operations Implementation Outer Join Aggregations Evaluating Expressions Pipelining Logistics Course link...

An introduction to solid state physics. Logistics Heat Capacity of Solids Einstein Model of Heat Capacity of Solids Debye Model of Heat Capacity of Solids Electrical Properties (Drude Model) Constant E&M Force Thermal Conductivity Sommerfield Model Fermi-Dirac Statistics Sommerfield Model (cont.) LCAO (Linear Combination of Atomic Orbitals)/ Tight Binding Theory Chemistry Review Shell Theory Ionic Bonds Covalent Bonds LCAO Basics Vibrations 2 Types of Springs Crystal Structure Reciprocal Space Logistics Location: 307 Pupin Time: 2:40-3:55 PM Tuesdays and Thursdays Textbook: The Oxford Solid State Basics Grading Scheme 30% problem sets (5 in total....