diff --git a/algebre_1_td_1.tex b/algebre_1_td_1.tex
new file mode 100644
index 0000000..6fad136
--- /dev/null
+++ b/algebre_1_td_1.tex
@@ -0,0 +1,210 @@
+\documentclass{article}
+
+\usepackage{mathtools}
+\usepackage{amssymb}
+
+\title{Algèbre 1 - TD 1 \\ NON CORRIGÉ}
+\author{Timéo Pochin}
+
+\begin{document}
+    \maketitle
+
+    \section*{Exercice 1}
+
+    \subsection*{1)}
+    \begin{align}
+        & \neg ( P \land \neg Q ) \nonumber \\
+    \iff\quad & \neg P \lor Q \nonumber
+    \end{align}
+
+    \subsection*{2)}
+    \begin{align}
+        & \neg\big(P\land (Q\land R)\big) \nonumber \\
+    \iff\quad & \neg ( P \land Q \land R ) \nonumber \\
+    \iff\quad & \neg P \lor \neg Q \lor \neg R \nonumber
+    \end{align}
+
+    \subsection*{3)}
+    \begin{align}
+        & \neg\big(P\lor (Q\land R)\big) \nonumber \\
+    \iff\quad & \neg P \land \neg (Q \land R) \nonumber \\
+    \iff\quad & \neg P \land (\neg Q \lor \neg R) \nonumber
+    \end{align}
+
+    \subsection*{4)}
+    \begin{align}
+        & \neg\big((P\land Q)\Rightarrow(R\Rightarrow S)\big) \nonumber \\
+    \iff\quad & P \land Q \land \neg (R \Rightarrow S) \nonumber \\
+    \iff\quad & P \land Q \land R \land \neg S \nonumber
+    \end{align}
+
+    \section*{Exercice 2}
+
+    \subsection*{}
+    \begin{tabular}{ |c|c|c||c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $\neg P$ & $\neg Q$ & $\neg P \Leftrightarrow \neg Q$ \\ \hline
+        \hline
+        F & F & F & V & V & V \\ \hline
+        F & F & V & V & V & V \\ \hline
+        V & V & F & F & F & V \\ \hline
+        V & V & V & F & F & V \\ \hline
+    \end{tabular}
+
+    \subsection*{}
+    \begin{tabular}{ |c|c|c||c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $P\Rightarrow R$ & $Q\Rightarrow R$ & $(P\Rightarrow R)\Leftrightarrow(Q\Rightarrow R)$ \\ \hline
+        \hline
+        F & F & F & V & V & V \\ \hline
+        F & F & V & V & V & V \\ \hline
+        V & V & F & F & F & V \\ \hline
+        V & V & V & V & V & V \\ \hline
+    \end{tabular}
+
+    \subsection*{}
+    \begin{tabular}{ |c|c|c||c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $R\Rightarrow P$ & $R\Rightarrow Q$ & $(R\Rightarrow P)\Leftrightarrow(R\Rightarrow Q)$ \\ \hline
+        \hline
+        F & F & F & V & V & V \\ \hline
+        F & F & V & F & F & V \\ \hline
+        V & V & F & V & V & V \\ \hline
+        V & V & V & V & V & V \\ \hline
+    \end{tabular}
+
+    \subsection*{}
+    \begin{tabular}{ |c|c|c||c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $P\land R$ & $Q\land R$ & $(P\land R)\Leftrightarrow(Q\land R)$ \\ \hline
+        \hline
+        F & F & F & F & F & V \\ \hline
+        F & F & V & F & F & V \\ \hline
+        V & V & F & F & F & V \\ \hline
+        V & V & V & V & V & V \\ \hline
+    \end{tabular}
+
+    \subsection*{}
+    \begin{tabular}{ |c|c|c||c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $P\lor R$ & $Q\lor R$ & $(P\lor R)\Leftrightarrow(Q\lor R)$ \\ \hline
+        \hline
+        F & F & F & F & F & V \\ \hline
+        F & F & V & V & V & V \\ \hline
+        V & V & F & V & V & V \\ \hline
+        V & V & V & V & V & V \\ \hline
+    \end{tabular}
+
+    \section*{Exercice 3}
+
+    \subsection*{1)}
+    \begin{tabular}{ |c|c||c|c|c|c|c|c| }
+        \hline
+        $P$ & $Q$ & $P\lor Q$ & $\neg(P\lor Q)$ & $\neg P$ & $\neg Q$ & $\neg P\land\neg Q$ & $\neg(P\lor Q)\Leftrightarrow\neg P\land\neg Q$ \\ \hline
+        \hline
+        F & F & F & V & V & V & V & V \\ \hline
+        F & V & V & F & V & F & F & V \\ \hline
+        V & F & V & F & F & V & F & V \\ \hline
+        V & V & V & F & F & F & F & V \\ \hline
+    \end{tabular}
+
+    \subsection*{2)}
+    \begin{tabular}{ |c|c|c||c|c|c|c|c| }
+        \hline
+        $P$ & $Q$ & $R$ & $P\Rightarrow Q$ & $Q\Rightarrow R$ & $(P\Rightarrow Q)\land(Q\Rightarrow R)$ & $P\Rightarrow R$ & $\big((P\Rightarrow Q)\land(Q\Rightarrow R)\big)\Rightarrow(P\Rightarrow R)$ \\ \hline
+        \hline
+       %P   Q   R
+        F & F & F & V & V & V & V & V \\ \hline
+        F & F & V & V & V & V & V & V \\ \hline
+        F & V & F & V & F & F & V & V \\ \hline
+        F & V & V & V & V & V & V & V \\ \hline
+        V & F & F & F & V & F & F & V \\ \hline
+        V & F & V & F & V & F & V & V \\ \hline
+        V & V & F & V & F & F & F & V \\ \hline
+        V & V & V & V & V & V & V & V \\ \hline
+    \end{tabular}
+
+    \section*{Exercice 4}
+
+    \subsection*{1)}
+    \begin{align}
+         & (P\land Q)\Rightarrow P \nonumber \\
+    \iff\quad & \neg(P\land Q)\lor P \nonumber \\
+    \iff\quad & \neg P\lor\neg Q\lor P \nonumber \\
+    \iff\quad & \text{Vrai}\lor\neg Q \nonumber \\
+    \iff\quad & \text{Vrai} \nonumber
+    \end{align}
+
+    \subsection*{2)}
+    \begin{align}
+         & \bigg(\big(P\Rightarrow(Q\Rightarrow R)\big)\Leftrightarrow\big((P\land Q)\Rightarrow R\big)\bigg) \nonumber \\
+    \iff\quad & \bigg(\big(\neg P\lor(Q\Rightarrow R)\Leftrightarrow\neg(P\land Q)\lor R\big)\bigg) \nonumber \\
+    \iff\quad & (\neg P\lor\neg Q\lor R\Leftrightarrow\neg P\lor\neg Q\lor R) \nonumber \\
+    \iff\quad & \text{Vrai} \nonumber
+    \end{align}
+
+    \subsection*{3)}
+    \begin{align}
+         & \bigg(\big((P\land Q)\Rightarrow R\big)\Leftrightarrow\big(\neg P\lor(Q\Rightarrow R)\big)\bigg) \nonumber \\
+    \iff\quad & \bigg(\big(\neg(P\land Q)\lor R\big)\Leftrightarrow(\neg P\lor\neg Q\lor R)\bigg) \nonumber \\
+    \iff\quad & \big((\neg P\lor\neg Q\lor R)\Leftrightarrow(\neg P\lor\neg Q\lor R)\big) \nonumber \\
+    \iff\quad & \text{Vrai} \nonumber
+    \end{align}
+
+    \section*{Exercice 5}
+
+    \subsection*{1)}
+    Faux
+
+    \subsection*{2)}
+    Vrai
+
+    \subsection*{3)}
+    Faux
+
+    \section*{Exercice 6}
+
+    \subsection*{1)}
+    Il existe un triangle rectangle qui ne possède pas un angle droit.
+
+    \subsection*{2)}
+    Il existe une maison où au moins un enfant n’aime pas ses deux parents.
+
+    \subsection*{3)}
+    Il existe un entier $x$ tel que, pour tout entier $y$, pour tout entier $z$, la relation $z\geq x+1$ implique la relation $z\geq y$.
+
+    \subsection*{4)}
+    \[
+    \exists\epsilon>0,\quad \forall\alpha>0,\quad |5x-7|\geq\epsilon\Rightarrow|x-\frac{7}{5}|\geq\alpha
+    \]
+
+    \section*{Exercice 7}
+
+    \subsection*{1)}
+    \[
+    \forall n\in\mathbb{R}^+,\quad \exists a\in\{x\in\mathbb{R}\mid-n<x<n\},\quad a\in A
+    \]
+
+    \subsection*{2)}
+    \[
+    \{0\}
+    \]
+
+    \subsection*{3)}
+    \[
+    \{1\}
+    \]
+
+    \section*{Exercice 8}
+
+    \subsection*{1)}
+    Pour tout entier naturel $n$, il existe un entier naturel $p$ tel que, $n$ est plus petit ou égal à $p$.
+    \\\\
+    Il existe un entier naturel $n$ tel que, pour tout entier naturel $p$, $n$ est plus grand que $p$.
+
+    \subsection*{2)}
+    Pour tout entier naturel $p$, pour tout entier négatif $n$, $p$ est plus grand ou égal à $n$.
+    \\\\
+    Il existe un entier naturel $p$ et un entier négatif $n$ tel que, $p$ est plus petit que $n$.
+
+\end{document}
diff --git a/analyse_1_td_1.tex b/analyse_1_td_1.tex
index d6ec8bb..7526a82 100644
--- a/analyse_1_td_1.tex
+++ b/analyse_1_td_1.tex
@@ -12,24 +12,83 @@
     \section*{Exercice 1}
 
     \subsection*{a)}
+    \begin{align}
+              & 5x+2\geq-3 \nonumber \\
+    \iff\quad & 5x\geq-5 \nonumber \\
+    \iff\quad & x\geq-1 \nonumber \\
+    \iff\quad & x=\left[-1,+\infty\right[ \nonumber
+    \end{align}
 
     \subsection*{b)}
+    \begin{align}
+              & 2x-1<4x+3\leq-x+6 \nonumber \\
+    \iff\quad & (2x-1<4x+3)\land(4x+3\leq-x+6) \nonumber \\
+    \iff\quad & (-4<2x)\land(5x\leq 3) \nonumber \\
+    \iff\quad & (-2<x)\land(x\leq\frac{3}{5}) \nonumber \\
+    \iff\quad & x=\left]-2,\frac{3}{5}\right] \nonumber
+    \end{align}
 
     \subsection*{c)}
+    \begin{align}
+              & |x-1|<4 \nonumber \\
+    \iff\quad & (x-1<4)\land(x-1>-4) \nonumber \\
+    \iff\quad & (x<5)\land(x>-3) \nonumber \\
+    \iff\quad & x=\left]-3,5\right[ \nonumber
+    \end{align}
 
     \subsection*{d)}
+    \begin{align}
+              & |x-2|\geq 3 \nonumber \\
+    \iff\quad & (x-2\geq 3)\lor(x-2\leq-3) \nonumber \\
+    \iff\quad & (x\geq 5)\lor(x\leq-1) \nonumber \\
+    \iff\quad & x=\left]-\infty,-1\right]\ \cup\ \left[5,+\infty\right[ \nonumber
+    \end{align}
 
     \subsection*{e)}
+    \begin{align}
+              & |x-2|\leq|x| \nonumber \\
+    \iff\quad & (x-2)^2\leq x^2 \nonumber \\
+    \iff\quad & x^2-4x+4\leq x^2 \nonumber \\
+    \iff\quad & 4\leq 4x \nonumber \\
+    \iff\quad & 1\leq x \nonumber \\
+    \iff\quad & x=\left[1,+\infty\right[ \nonumber
+    \end{align}
 
     \subsection*{f)}
 
     \subsection*{g)}
+    \begin{align}
+              & \sqrt{x+1}<2 \nonumber \\
+    \iff\quad & (x+1<4)\land(x+1\geq0) \nonumber \\
+    \iff\quad & (x<3)\land(x\geq-1) \nonumber \\
+    \iff\quad & x=\left[-1,3\right[ \nonumber
+    \end{align}
 
     \subsection*{h)}
+    \begin{align}
+              & x^2+1\leq 3 \nonumber \\
+    \iff\quad & x^2\leq 2 \nonumber \\
+    \iff\quad & (x\leq\sqrt{2})\land(x\geq-\sqrt{2}) \nonumber \\
+    \iff\quad & x=\left[-\sqrt{2},\sqrt{2}\right] \nonumber
+    \end{align}
 
     \subsection*{i)}
+    \begin{align}
+              & x^2+3x<4 \nonumber \\
+    \iff\quad & x^2+3x-4<0 \nonumber \\
+    \iff\quad & (x-1)(x+4)<0 \nonumber \\
+    \iff\quad & (x<1)\land(x>-4) \nonumber \\
+    \iff\quad & x=\left]-4,1\right[ \nonumber
+    \end{align}
 
     \subsection*{j)}
+    \begin{align}
+              & x^3-3x^2+2x\geq 0 \nonumber \\
+    \iff\quad & x(x^2-3x+2)\geq 0 \nonumber \\
+    \iff\quad & x(x-1)(x-2)\geq 0 \nonumber \\
+    \iff\quad & \big((x\geq 0)\land(x\leq 1)\big)\lor(x\geq 2) \nonumber \\
+    \iff\quad & x=\left[0,1\right]\cup\left[2,+\infty\right[ \nonumber
+    \end{align}
 
     \subsection*{k)}
 
diff --git a/mecanique_du_point_td_1.tex b/mecanique_du_point_td_1.tex
new file mode 100644
index 0000000..44e3fc5
--- /dev/null
+++ b/mecanique_du_point_td_1.tex
@@ -0,0 +1,268 @@
+\documentclass{article}
+
+\usepackage{mathtools}
+\usepackage{amssymb}
+
+\title{Mécanique du point - TD 1 \\ NON CORRIGÉ}
+\author{Timéo Pochin}
+
+\begin{document}
+    \maketitle
+
+    \section*{Exercice 1}
+
+    \subsection*{a)}
+    \begin{align}
+    \vec{u}\land\vec{v}
+    \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        4 \\
+        5 \\
+        6
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        2\cdot 6-5\cdot 3 \\
+        4\cdot 3-1\cdot 6 \\
+        1\cdot 5-4\cdot 2
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        -3 \\
+        6 \\
+        -3
+    \end{pmatrix}
+    \\ \nonumber
+    &=-3\vec{e_x}+6\vec{e_y}-3\vec{e_z}
+    \end{align}
+
+    \subsection*{b)}
+    \begin{align}
+    \vec{v}\land\vec{u}
+    \nonumber
+    &=
+    \begin{pmatrix}
+        4 \\
+        5 \\
+        6
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        5\cdot 3-2\cdot 6 \\
+        1\cdot 6-4\cdot 3 \\
+        4\cdot 2-1\cdot 5
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        3 \\
+        -6 \\
+        3
+    \end{pmatrix}
+    \\ \nonumber
+    &=3\vec{e_x}-6\vec{e_y}+3\vec{e_z}
+    \end{align}
+
+    \subsection*{c)}
+    \begin{align}
+    \vec{u}\cdot\vec{v}
+    \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \cdot
+    \begin{pmatrix}
+        4 \\
+        5 \\
+        6
+    \end{pmatrix}
+    \\ \nonumber
+    &=1\cdot 4+2\cdot 5+3\cdot 6\\ \nonumber
+    &=32
+    \end{align}
+
+    \subsection*{d)}
+    \begin{align}
+    \vec{u}\cdot(\vec{u}\land\vec{v})
+    \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \cdot
+    \begin{pmatrix}
+        -3 \\
+        6 \\
+        -3
+    \end{pmatrix}
+    \\ \nonumber
+    &=1\cdot-3+2\cdot 6+3\cdot -3\\ \nonumber
+    &=0
+    \end{align}
+
+    \subsection*{e)}
+    \begin{align}
+    \|\vec{u}\|
+    \nonumber
+    &=\sqrt{1^2+2^2+3^2}
+    \\ \nonumber
+    &=\sqrt{14}
+    \end{align}
+
+    \subsection*{f)}
+    \begin{align}
+    \|\vec{u}+\vec{v}\|
+    \nonumber
+    &=
+    \left\|
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    +
+    \begin{pmatrix}
+        4 \\
+        5 \\
+        6
+    \end{pmatrix}
+    \right\|
+    \\ \nonumber
+    &=
+    \left\|
+    \begin{pmatrix}
+        5 \\
+        7 \\
+        9
+    \end{pmatrix}
+    \right\|
+    \\ \nonumber
+    &=\sqrt{5^2+7^2+9^2}
+    \\ \nonumber
+    &=\sqrt{155}
+    \end{align}
+
+    \subsection*{g)}
+    \begin{align}
+    (\vec{u}\land\vec{v})\land\vec{w}
+    \nonumber
+    &=
+    \begin{pmatrix}
+        -3 \\
+        6 \\
+        -3
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        7 \\
+        8 \\
+        9
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        6\cdot 9-8\cdot-3 \\
+        7\cdot-3-9\cdot-3 \\
+        -3\cdot 8-7\cdot 6
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        78 \\
+        6 \\
+        -66
+    \end{pmatrix}
+    \\ \nonumber
+    &=78\vec{e_x}+6\vec{e_y}-66\vec{e_z}
+    \end{align}
+
+    \subsection*{h)}
+    \begin{align}
+    \vec{u}\land(\vec{v}\land\vec{w})
+    \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \land
+    \left(
+    \begin{pmatrix}
+        4 \\
+        5 \\
+        6
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        7 \\
+        8 \\
+        9
+    \end{pmatrix}
+    \right)
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        5\cdot 9-8\cdot 6 \\
+        7\cdot 6-4\cdot 9 \\
+        4\cdot 8-7\cdot 5
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        1 \\
+        2 \\
+        3
+    \end{pmatrix}
+    \land
+    \begin{pmatrix}
+        -3 \\
+        6 \\
+        -3
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        2\cdot-3-6\cdot 3 \\
+        -3\cdot 3-1\cdot-3 \\
+        1\cdot 6--3\cdot 3
+    \end{pmatrix}
+    \\ \nonumber
+    &=
+    \begin{pmatrix}
+        -24 \\
+        -6 \\
+        12
+    \end{pmatrix}
+    \\ \nonumber
+    &= -24\vec{e_x}-6\vec{e_y}+12\vec{e_z}
+    \end{align}
+
+\end{document}
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