physiology and pharmacology experiments
in virtual laboratories
almost like in the real world
- Perfect for online teaching and remote learning -
Master the Proofs: Surviving and Fixing Your Experience in 6120A Discrete Mathematics and Proof for Computer Science
Do not just look at a graded homework assignment, sigh at the lost points, and shove it in a folder.
A password must be 8 characters long, containing at least one digit and at least one uppercase letter. How many such passwords can be formed from a 62-character alphabet (0-9, a-z, A-Z)? 8. Inclusion-Exclusion:
Before submitting any proof, check: ☐ Is the proof type (direct, contrapositive, contradiction, induction) clearly stated? ☐ Are all variables introduced? (“Let (x) be an arbitrary integer…”) ☐ Is each step justified by a definition, axiom, or previous step? ☐ Did I avoid starting with what I need to prove? ☐ Is the concluding sentence present? (“Therefore, (P \to Q) holds.”)
Drawing a specific graph and assuming all graphs of that type share the exact same edge behavior.
. Tip: Always explicitly state where you use the Inductive Hypothesis in your algebra. Combinatorics and Counting
: Mastering the syntax of mathematical notation to translate complex technical ideas between English and formal logic. Foundational Tools : Developing a "toolbox" for advanced CS courses like MIT's Design and Analysis of Algorithms Key Subject Areas The curriculum typically divides into three main pillars: MIT - Massachusetts Institute of Technology Syllabus | Mathematics for Computer Science
Master truth tables early. Do not just memorize them; understand why is true when
If you are struggling with the transition to formal proofs, falling behind on p-sets, or failing to see how sets and state machines apply to software engineering, you need a strategic correction. This guide provides an actionable, comprehensive "fix" to master the logical frameworks, proof templates, and problem-solving strategies required to ace 6.120A. Why 6.120A Feels "Broken" (And How to Shift Your Mindset)
- Writing a "convoluted and obtuse" proof will lose points even if technically correct. Clear, concise logical steps are key. Essential Resources for Success
It’s easy to feel like CS 6120A is "useless" math, but it is actually the foundation of high-level engineering: is the basis of circuit design and boolean search.
Translating natural language to logical symbols (like ∀for all ∃there exists
6.120a Discrete Mathematics and Proof for Computer Science: Fixing Common Misconceptions and Mastering the Core
Prove that a binary tree with n nodes has exactly n+1 null children. Proof by induction on n using tree structure.
Step 1: Build an Internal Compiler (The Write-Read-Verify Loop)
running on all Windows platforms,
from Win 7 to Win 11, 32 bit as well as 64 bit versions
without any specific requirements (see Technical Specifications)
including platform-independent Online Versions
for experiments via the Virtual Physiology server
existing so far for SimHeart and SimVessel
with beta-versions of SimMuscle and SimNeuron
SimHeart offers a virtual laboratory for recordings of heart contractions in the Langendorff set-up in response on the most relevant transmitters and drugs, including a drug laboratory for the adjustment of the appropriate solutions.
SimVessel offers a virtual laboratory for the examination of smooth muscle contractions of vessels and the intestine.
The experiments can be done with muscle stripes, placed in an organ bath to which physiologically relevant signal substances and widely used drugs can be added. Preparing the appropriate dilutions can be trained, as in SimHeart, in a drug laboratory.
The virtual “SimMuscle” laboratory contains two nerve-muscle preparations and all the apparatus that you will need for experimentation in a simplified but quite realistic form.
When entering the lab you first need to switch on all the devices (POWER buttons). Then drag one of two already prepared nerve-muscle preparations from the Petri-dish to hang it in the suspension apparatus. This includes a mechano-electrical converter transforming changes of either the muscle force or muscle length, selectable by a toggle switch, into an electric potential. You can pre-stretch the muscle hanging one or more weights in the loop at which the muscle is fixed.
Muscle contractions are induced by current pulses delivered from a stimulation apparatus to the electrodes on which the nerve is placed. Stimuli as well as muscle contractions are displayed on a dual beam storage oscilloscope, appropriately displayed with accordingly adjusted voltage amplification and time base (via the rotary switches) and zero lines. Single or double pulses as well as trains of stimuli of selectable amplitude and intervals can be applied.
The example shows muscle contractions, here changes of the muscle length, in response to different trains of voltage pulses inducing isolated twitches, incomplete and complete tetanic contractions depending on the intervals in which the pulses are applied.
Master the Proofs: Surviving and Fixing Your Experience in 6120A Discrete Mathematics and Proof for Computer Science
Do not just look at a graded homework assignment, sigh at the lost points, and shove it in a folder.
A password must be 8 characters long, containing at least one digit and at least one uppercase letter. How many such passwords can be formed from a 62-character alphabet (0-9, a-z, A-Z)? 8. Inclusion-Exclusion:
Before submitting any proof, check: ☐ Is the proof type (direct, contrapositive, contradiction, induction) clearly stated? ☐ Are all variables introduced? (“Let (x) be an arbitrary integer…”) ☐ Is each step justified by a definition, axiom, or previous step? ☐ Did I avoid starting with what I need to prove? ☐ Is the concluding sentence present? (“Therefore, (P \to Q) holds.”)
Drawing a specific graph and assuming all graphs of that type share the exact same edge behavior.
. Tip: Always explicitly state where you use the Inductive Hypothesis in your algebra. Combinatorics and Counting
: Mastering the syntax of mathematical notation to translate complex technical ideas between English and formal logic. Foundational Tools : Developing a "toolbox" for advanced CS courses like MIT's Design and Analysis of Algorithms Key Subject Areas The curriculum typically divides into three main pillars: MIT - Massachusetts Institute of Technology Syllabus | Mathematics for Computer Science
Master truth tables early. Do not just memorize them; understand why is true when
If you are struggling with the transition to formal proofs, falling behind on p-sets, or failing to see how sets and state machines apply to software engineering, you need a strategic correction. This guide provides an actionable, comprehensive "fix" to master the logical frameworks, proof templates, and problem-solving strategies required to ace 6.120A. Why 6.120A Feels "Broken" (And How to Shift Your Mindset)
- Writing a "convoluted and obtuse" proof will lose points even if technically correct. Clear, concise logical steps are key. Essential Resources for Success
It’s easy to feel like CS 6120A is "useless" math, but it is actually the foundation of high-level engineering: is the basis of circuit design and boolean search.
Translating natural language to logical symbols (like ∀for all ∃there exists
6.120a Discrete Mathematics and Proof for Computer Science: Fixing Common Misconceptions and Mastering the Core
Prove that a binary tree with n nodes has exactly n+1 null children. Proof by induction on n using tree structure.
Step 1: Build an Internal Compiler (The Write-Read-Verify Loop)
SimNeuron offers virtual laboratories for voltage- and current-clamp experiments in an easy to overlook lab design
In fully licensed versions there is the possibility to select to which specific features of the program the students shall have access. This can be done in so-called pre-settings window which you can open from the labs via the SETTINGS button in the switch bank. In demo versions the pre-settings are fixed with most functions enabled. This guide provides an actionable
