fixing mathjax syntax

docs/RESOURCES.md

@@ -8,6 +8,7 @@
 |                          | *Organic Chemistry, 6th Edition*                   | Book                  | Janice Gorzynski Smith, another recommended text|
 |                          | *Any Organic Chemistry textbook*                   | Book                  | General recommendation from course             |
 | **Software**              | [**ChemDraw**](https://www.perkinelmer.com/category/chemdraw) | Software | Tool for visualizing chemical structures       |
+|                           | [**PTable**](https://ptable.com/) | Web app | Interactive periodic table |
 | **Courses & Tutorials**   | [**Organic Chemistry Course on MyAriel**](https://myariel.unimi.it/course/view.php?id=4257) | Course Website | Official course page for Organic Chemistry     |
 |                          | [**YouTube: Shells, Subshells, and Orbitals**](https://www.youtube.com/watch?v=UDmrRWeFWwU) | Video Tutorial | Simple video explaining atomic structure       |
 |                          | [**MinutePhysics: A Better Way To Picture Atoms**](https://www.youtube.com/watch?v=W2Xb2GFK2yc) | Video Tutorial | Visualization of atomic structure and behavior |

docs/lectures/biochemistry/lesson-1.md

@@ -97,15 +97,15 @@ In biomolecules, functional groups are essential for dictating how molecules int
 
 These groups typically replace hydrogen atoms in hydrocarbons, giving rise to molecules with diverse chemical behaviors.
 
-- **Variety of carbon** ($ \text{C} $): Carbon's ability to form covalent single, double, and occasionally triple bonds makes it incredibly versatile.
+- **Variety of carbon** ($\text{C}$): Carbon's ability to form covalent single, double, and occasionally triple bonds makes it incredibly versatile.
     - In biological molecules, this means carbon can create stable, complex structures essential for life, such as chains and rings, which serve as backbones for biomolecules.
 
 - **Formation of 4 stable single bonds**: Carbon can form up to four stable single covalent bonds with other atoms, including other carbon atoms.
     - This property allows the formation of long carbon chains and branched structures, which are foundational to many biomolecules like carbohydrates, lipids, and proteins.
     - Biomolecules as hydrocarbons: Biomolecules can be thought of as hydrocarbons (compounds made of hydrogen and carbon). In most biomolecules, some of the hydrogen atoms are replaced by functional groups, such as:
-        - hydroxyl $ \text{-OH} $
-        - carboxyl $ \text{-COOH} $
-        - amino $ \text{-NH}_2 $
+        - hydroxyl $\text{-OH}$
+        - carboxyl $\text{-COOH}$
+        - amino $\text{-NH}_2$
 
         Giving the molecules distinct properties and reactivity.
 

docs/lectures/bioinformatics-and-computational-biology/introduction.md

@@ -12,7 +12,7 @@ In alternative, the following extended defition could be considered:
 
 - Bioinformatics is an interdisciplinary field that combines biology, computer science, mathematics, and statistics to analyze and interpret biological data, especially large datasets. It primarily involves developing algorithms, computational models, and software tools to understand biological processes and systems.
 
-### Definition of **Computational Biology** (according to the $ \text{NIH} $)
+### Definition of **Computational Biology** (according to the $\text{NIH}$)
 
 Computational Biology refers to the development and application of data-analytical and theoretical methods, mathematical modeling and
 computational simulation tecniques to the study of biological, behavioral and, social systems.

docs/lectures/organic-chemistry/lesson-4_24-09-2024.md

@@ -8,11 +8,11 @@
 
 - A functional group is an **atom** or a **group of atoms** with characteristic chemical and physical properties.
 
-- Most organic molecules contain a carbon backbone, consisting of $\ce{C-C}$ and $\ce{C-H}$ bonds to which functional groups are attached.
+- Most organic molecules contain a carbon backbone, consisting of $\ce{C-C}$and$\ce{C-H}$ bonds to which functional groups are attached.
 
 - Structural features of a functional group:
-    - **Heteroatoms** $\rightarrow$ atoms other than $\ce{C}$ or $\ce{H}$
-    - Bonds commonly occur in $\ce{C-C}$ and $\ce{C-O}$ double bonds
+    - **Heteroatoms** $\rightarrow$atoms other than$\ce{C}$or$\ce{H}$
+    - Bonds commonly occur in $\ce{C-C}$and$\ce{C-O}$ double bonds
 
 Functional groups distinguish one organic molecule from another, they're able to determine a molecule's:
 - Name
@@ -44,7 +44,7 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule
 
 - The $\pi$ bond is easily broken.
 - The $\pi$ bond makes a compound a base and a nucleophile.
-    - In many chemical reactions, especially in **nucleophilic substitution** or **addition reactions**, the $\pi$ bond donates its electrons to form new bonds. Since the $\pi$ bond is more loosely held, it can be broken, allowing the electrons to be used in new bond formation with other atoms or groups.
+    - In many chemical reactions, especially in **nucleophilic substitution** or **addition reactions**, the $\pi$bond donates its electrons to form new bonds. Since the$\pi$ bond is more loosely held, it can be broken, allowing the electrons to be used in new bond formation with other atoms or groups.
 
 #### Why $\pi$ bonds break so easily
 
@@ -66,11 +66,11 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule
 </p>
 
 - **Ethane**
-    - Has all $\ce{C-C}$ and $\ce{C-H}$ $\sigma$ bonds
+    - Has all $\ce{C-C}$and$\ce{C-H}$ $\sigma$ bonds
     - Has no functional group
 
 - **Ethanol**
-    - Polar $\ce{C-O}$ and $\ce{O-H}$ bonds
+    - Polar $\ce{C-O}$and$\ce{O-H}$ bonds
     - Two lone pairs
 
 # Ethane, a Molecule with No Functional Group
@@ -89,7 +89,7 @@ Heteratoms and bonds are responsible for the reactivity on a particular molecule
 
 **NOTE**: The term **"backbone"** is used to describe the continuous chain of atoms that provides the main structure, to which other atoms or groups can be attached, influencing the molecule’s properties.
 
-Ethane consists of **nonpolar $\ce{C-C}$ and weakly polar $\ce{C-H}$ bonds**, resulting in no significant reactive sites. It lacks functional groups and lone pairs, making it **chemically inert** under normal conditions and requiring high energy (e.g., combustion) to break its bonds. On the other hand, Ethanol has a **hydroxyl group ($\ce{-OH}$)**, making it much more reactive than ethane. The **polar $\ce{O-H}$ and $\ce{C-O}$ bonds** create partial charges, making the molecule susceptible to **nucleophilic and electrophilic attacks**. The hydroxyl group also enables ethanol to undergo various reactions (e.g., **oxidation**, **dehydration**, **esterification**) and form **hydrogen bonds**, increasing its overall reactivity.
+Ethane consists of **nonpolar $\ce{C-C}$and weakly polar$\ce{C-H}$ bonds**, resulting in no significant reactive sites. It lacks functional groups and lone pairs, making it **chemically inert** under normal conditions and requiring high energy (e.g., combustion) to break its bonds. On the other hand, Ethanol has a **hydroxyl group ($\ce{-OH}$)**, making it much more reactive than ethane. The **polar $\ce{O-H}$and$\ce{C-O}$ bonds** create partial charges, making the molecule susceptible to **nucleophilic and electrophilic attacks**. The hydroxyl group also enables ethanol to undergo various reactions (e.g., **oxidation**, **dehydration**, **esterification**) and form **hydrogen bonds**, increasing its overall reactivity.
 
 ### Hydrocarbons
 
@@ -100,9 +100,9 @@ Hydrocarbons are compounds make up of only the elements carbon and hydrogen; the
 </p>
 
 - Aliphatic hydrocarbons have three subgroups 
-    - Alkanes have only $\ce{C-C}$ bonds and no functional group $\rightarrow \ce{C-C}$
-    - Alkenes have a $\ce{C-C}$ double bond $\rightarrow \ce{C=C}$
-    - Alkynes have a $\ce{C-C}$ triple bond $\rightarrow \ce{C#C}$ 
+    - Alkanes have only $\ce{C-C}$bonds and no functional group$\rightarrow \ce{C-C}$
+    - Alkenes have a $\ce{C-C}$double bond$\rightarrow \ce{C=C}$
+    - Alkynes have a $\ce{C-C}$triple bond$\rightarrow \ce{C#C}$ 
 
 ### Aromatic hydrocarbons
 
@@ -121,7 +121,7 @@ Hydrocarbons are compounds make up of only the elements carbon and hydrogen; the
     <img src="assets/c-z-sigma-bond.png" width=400/>
 </p>
 
-The structure on the right shows a 3D molecular model where carbon is bonded to the heteroatom $\ce{Z}$ with an arrow indicating the direction of the electron density being pulled toward the more electronegative atom $\ce{Z}$.
+The structure on the right shows a 3D molecular model where carbon is bonded to the heteroatom $\ce{Z}$with an arrow indicating the direction of the electron density being pulled toward the more electronegative atom$\ce{Z}$.
 - This type of bond is common in many functional groups like alcohols C—O, amines C—N, and halides C—Cl, C—Br, etc.
 
 > **What's a halogen? a halide?**
@@ -134,7 +134,7 @@ The structure on the right shows a 3D molecular model where carbon is bonded to
 ### Functional groups with $\ce{C-O}$ group 
 
 - This group is called a "carbonyl group"
-- The polar $\ce{C=O}$ bond makes the carbonyl carbon an electrophile, while the lone pairs on $\ce{O}$ allow it to react as a nucleophile and base
+- The polar $\ce{C=O}$bond makes the carbonyl carbon an electrophile, while the lone pairs on$\ce{O}$ allow it to react as a nucleophile and base
 
 <p align="center">
     <img src="assets/carbonyl-group.png" width="300"/>
@@ -191,7 +191,7 @@ Intermolecular forces are interactions that exist between molecules, functional
 
 #### Ion-Ion interactions
 
-In an ionic compound, such as sodium chloride $\ce{NaCl}$, the positively charged sodium ions $\ce{Na}^+$ and negatively charged chloride ions $\ce{Cl}^-$ are arranged in a repeating lattice structure. The ions are held together by the **electrostatic forces** of attraction between opposite charges.
+In an ionic compound, such as sodium chloride $\ce{NaCl}$, the positively charged sodium ions $\ce{Na}^+$and negatively charged chloride ions$\ce{Cl}^-$ are arranged in a repeating lattice structure. The ions are held together by the **electrostatic forces** of attraction between opposite charges.
 
 **Sidenote**: This strong interaction is responsible for the high melting and boiling points of ionic compounds because a significant amount of energy is required to break these strong bonds.
 
@@ -222,7 +222,7 @@ While van der Waals forces are weak, **they are significant in large numbers**.
 
 The strength of van der Waals forces increases with the size and surface area of the molecule because larger molecules have more electrons and a greater ability to become polarized.
 
-**NOTE**: This is why larger nonpolar molecules like iodine $\ce{I_2}$ or long-chain hydrocarbons have higher boiling and melting points compared to smaller nonpolar molecules like helium $\ce{He}$ or methane ($\ce{CH_4}$).
+**NOTE**: This is why larger nonpolar molecules like iodine $\ce{I_2}$or long-chain hydrocarbons have higher boiling and melting points compared to smaller nonpolar molecules like helium$\ce{He}$ or methane ($\ce{CH_4}$).
 
 #### var der Waals forces in methane
 
@@ -288,22 +288,22 @@ Hydrogen bonding typically occurs when a hydrogen atom bonded to O, N, or F, is
 
 They vary in strength between $\text{5-25 kJ/mol}$ and are weaker than electrostatic interactions but definetely stronger than van der Waals interactions.
 
-- Hydrogen bonds take place between an electron deficient hydrogen and an electron rich heteroatom (typically $\ce{N}$ or $\ce{O}$). 
+- Hydrogen bonds take place between an electron deficient hydrogen and an electron rich heteroatom (typically $\ce{N}$or$\ce{O}$). 
 
-The electron deficient hydrogen is called a ***hydrogen bond donor*** $\rightarrow$ **HBD**. The electron rich heteroatom on the other hand is called a ***hydrogen bond acceptor*** $\rightarrow$ **HBA**.
+The electron deficient hydrogen is called a ***hydrogen bond donor*** $\rightarrow$**HBD**. The electron rich heteroatom on the other hand is called a ***hydrogen bond acceptor***$\rightarrow$ **HBA**.
 
 <p align="center">
     <img src="assets/hbd-hba.png" />
 </p>
 
-- $\ce{X-H}$ is a hydrogen bond donor (HBD), with the hydrogen being $\delta^+$.
-- $\ce{Y}$ is a hydrogen bond acceptor (HBA), with lone pairs of electrons $\delta^-$ to form hydrogen bonds.
+- $\ce{X-H}$is a hydrogen bond donor (HBD), with the hydrogen being$\delta^+$.
+- $\ce{Y}$is a hydrogen bond acceptor (HBA), with lone pairs of electrons$\delta^-$ to form hydrogen bonds.
 
 Typically, the acceptor is also an electronegative atom like oxygen, nitrogen, or fluorine.
 
 In this mechanism, a drug molecule may contain such donor or acceptor groups to interact with the target via hydrogen bonding. This interaction allows the drug to bind specifically to the target, which could be a protein, enzyme, or another biological macromolecule, thereby influencing the function of the target. 
 
-In hydrogen bonds the inteaction involves orbitals and is **directional**, optimum orientation is where the $\ce{X-H}$ bond points directly to the lone pair on $\ce{Y}$ such that the angle between X, H and Y is $\ce{180°}$
+In hydrogen bonds the inteaction involves orbitals and is **directional**, optimum orientation is where the $\ce{X-H}$bond points directly to the lone pair on$\ce{Y}$such that the angle between X, H and Y is$\ce{180°}$
 
 <p align="center">
     <img src="assets/drug-orientation-to-target.png" />
@@ -470,15 +470,15 @@ Most ionic compounds are soluble in water, but insoluble in organic solvents. To
 
 #### Solubility of organic molecules
 
-An organic molecule is water soluble only if it contains one polar functional group capable of hydrogen bonding with the solvent for every five $\ce{C}$ atoms in contains. Compare the solubility of butane and acetone in $\ce{H2O}$ and $\ce{CCl4}$
+An organic molecule is water soluble only if it contains one polar functional group capable of hydrogen bonding with the solvent for every five $\ce{C}$atoms in contains. Compare the solubility of butane and acetone in$\ce{H2O}$and$\ce{CCl4}$
 
 <p align="center">
     <img src="assets/butane-acetone-solubility.png" width=400 />
 </p>
 
 #### Butane and acetone solubility
 
-Since butane and acetone are both organic compounds, they are both soluble in the organic solvent $\ce{CCl4}$. Butane, which is nonpolar, is insoluble in $\ce{H2O}$. Acetone is soluble in $\ce{H2O}$ because it contains only three $\ce{C}$ atoms and its $\ce{O}$ atom can hydrogen bond with an $\ce{H}$ atom of $\ce{H2O}$.
+Since butane and acetone are both organic compounds, they are both soluble in the organic solvent $\ce{CCl4}$. Butane, which is nonpolar, is insoluble in $\ce{H2O}$. Acetone is soluble in $\ce{H2O}$because it contains only three$\ce{C}$atoms and its$\ce{O}$atom can hydrogen bond with an$\ce{H}$atom of$\ce{H2O}$.
 
 <p align="center">
     <img src="assets/butane-acetone-solubility-2.png" width=400 />
@@ -498,15 +498,15 @@ On the other hand, Cholesterol, with 27 carbon atoms and only one OH group, has
 | **Ionic**             |                       |                                                   |
 | $\ce{NaCl}$           | soluble               | insoluble                                         |
 | **Covalent**          |                       |                                                   |
-| $\ce{CH3CH2CH2CH3}$   | insoluble (no N or O atom to hydrogen bond to $\ce{H2O}$) | soluble |
-| $\ce{CH3CH2CH2OH}$    | soluble ($\leq 5$ C's and an O atom for hydrogen bonding to $\ce{H2O}$) | soluble |
-| $\ce{CH3(CH2)10OH}$   | insoluble ($> 5$ C's; too large to be soluble even though it has an O atom for hydrogen bonding to $\ce{H2O}$) | soluble |
+| $\ce{CH3CH2CH2CH3}$| insoluble (no N or O atom to hydrogen bond to$\ce{H2O}$) | soluble |
+| $\ce{CH3CH2CH2OH}$    | soluble ($\leq 5$C's and an O atom for hydrogen bonding to$\ce{H2O}$) | soluble |
+| $\ce{CH3(CH2)10OH}$   | insoluble ($> 5$C's; too large to be soluble even though it has an O atom for hydrogen bonding to$\ce{H2O}$) | soluble |
 
 ### Vitamins
 
 Vitamins are organic compunds needed in small amounts for normal cell function, most cannot be synthesized in our bodies and must be obtained from diet. Most are identified by a letter, such as A, C, D, E and K.
 
-There are several different B vitamins, so a subscript is added just to distinguish between them. Examples are $\ce{B_1}$, $\ce{B_2}$ and $\ce{B_12}$.
+There are several different B vitamins, so a subscript is added just to distinguish between them. Examples are $\ce{B_1}$, $\ce{B_2}$and$\ce{B_12}$.
 
 - Vitamins can be fat soluble or water soluble depending on their structure
 
@@ -551,7 +551,7 @@ A lone pair on a heteroatom makes it basic and nucleophilic
     <img src="assets/some-base-nucleophiles.png" width=400 />
 </p>
 
-$\pi$ bonds create nucleophilic sites and are more easily broken than $\sigma$ bonds.
+$\pi$bonds create nucleophilic sites and are more easily broken than$\sigma$ bonds.
 
 <p align="center">
     <img src="assets/nucleophiles-with-pibonds.png" width=400 />