typos

quarto/precalc/julia_overview.qmd

@@ -97,7 +97,7 @@ julia> 2 + 2
 
 
   * An IDE. For programmers, an integrated development environment is often used to manage bigger projects. `Julia` has `Juno` and `VSCode`.
-  * A notebook. The [Project Juptyer](https://jupyter.org/) provides a notebook interface for interacting with `Julia` and a more `IDE` style `jupyterlab` interface. A jupyter notebook has cells where commands are typed and immediately following is the printed output returned by `Julia`. The output of a cell depends on the state of the kernel when the cell is computed, not the order of the cells in the notebook. Cells have a number attached, showing the execution order. The `Juypter` notebook is used by `binder` and can be used locally through the `IJulia` package. This notebook has the ability to display many different types of outputs in addition to plain text, such as images, marked up math text, etc.
+  * A notebook. The [Project Jupyter](https://jupyter.org/) provides a notebook interface for interacting with `Julia` and a more `IDE` style `jupyterlab` interface. A jupyter notebook has cells where commands are typed and immediately following is the printed output returned by `Julia`. The output of a cell depends on the state of the kernel when the cell is computed, not the order of the cells in the notebook. Cells have a number attached, showing the execution order. The `Juypter` notebook is used by `binder` and can be used locally through the `IJulia` package. This notebook has the ability to display many different types of outputs in addition to plain text, such as images, marked up math text, etc.
   * The [Pluto](https://github.com/fonsp/Pluto.jl) package provides a *reactive* notebook interface. Reactive means when one "cell" is modified and executed, the new values cascade to all other dependent cells which in turn are updated. This is very useful for exploring a parameter space, say. Pluto notebooks can be exported as HTML files which make them easy to read online and – by clever design – embed the `.jl` file that can run through `Pluto` if it is downloaded.
 
 
@@ -280,7 +280,7 @@ Values will be promoted to a common type (or type `Any` if none exists). For exa
 (Vectors are used as a return type from some functions, as such, some familiarity is needed.)
 
 
-Other common container types are variables of vectors (higher-dimensional arrarys, offset arrays, etc.)  tuples (for heterogeneous, immutable, indexed values); named tuples (which add a name to each value in a tuple); and dictionaries (for associative relationships between a key and a value).
+Other common container types are variables of vectors (higher-dimensional arrays, offset arrays, etc.)  tuples (for heterogeneous, immutable, indexed values); named tuples (which add a name to each value in a tuple); and dictionaries (for associative relationships between a key and a value).
 
 
 Regular arithmetic sequences can be defined by either:

quarto/precalc/numbers_types.qmd

@@ -26,7 +26,7 @@ On top of these, we have special subsets, such as the natural numbers $\{1, 2, \
 Mathematically, these number systems are naturally nested within each other as integers are rational numbers which are real numbers, which can be viewed as part of the complex numbers.
 
 
-Calculators typically have just one type of number - floating point values. These model the real numbers. `Julia`, on the other hand, has a rich type system, and within that has serveral different number types. There are types that model each of the four main systems above, and within each type, specializations for how these values are stored.
+Calculators typically have just one type of number - floating point values. These model the real numbers. `Julia`, on the other hand, has a rich type system, and within that has several different number types. There are types that model each of the four main systems above, and within each type, specializations for how these values are stored.
 
 
 Most of the details will not be of interest to all, and will be described later.